Struct num_complex::Complex

#[repr(C)]
pub struct Complex<T> {
    pub re: T,
    pub im: T,
}

A complex number in Cartesian form.

Representation and Foreign Function Interface Compatibility

Complex<T> is memory layout compatible with an array [T; 2].

Note that Complex<F> where F is a floating point type is only memory layout compatible with C’s complex types, not necessarily calling convention compatible. This means that for FFI you can only pass Complex<F> behind a pointer, not as a value.

Examples

Example of extern function declaration.

use num_complex::Complex;
use std::os::raw::c_int;

extern "C" {
    fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>,
              x: *const Complex<f64>, incx: *const c_int,
              y: *mut Complex<f64>, incy: *const c_int);
}

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Implementations

impl<T> Complex<T>

pub const fn new(re: T, im: T) -> Self

Create a new Complex

impl<T: Clone + Num> Complex<T>

pub fn i() -> Self

Returns the imaginary unit.

See also Complex::I.

pub fn norm_sqr(&self) -> T

Returns the square of the norm (since T doesn’t necessarily have a sqrt function), i.e. re^2 + im^2.

pub fn scale(&self, t: T) -> Self

Multiplies self by the scalar t.

pub fn unscale(&self, t: T) -> Self

Divides self by the scalar t.

pub fn powu(&self, exp: u32) -> Self

Raises self to an unsigned integer power.

impl<T: Clone + Num + Neg<Output = T>> Complex<T>

pub fn conj(&self) -> Self

Returns the complex conjugate. i.e. re - i im

pub fn inv(&self) -> Self

Returns 1/self

pub fn powi(&self, exp: i32) -> Self

Raises self to a signed integer power.

impl<T: Clone + Signed> Complex<T>

pub fn l1_norm(&self) -> T

Returns the L1 norm |re| + |im| – the Manhattan distance from the origin.

impl<T: Float> Complex<T>

pub fn cis(phase: T) -> Self

Create a new Complex with a given phase: exp(i * phase). See cis (mathematics).

pub fn norm(self) -> T

Calculate |self|

pub fn arg(self) -> T

Calculate the principal Arg of self.

pub fn to_polar(self) -> (T, T)

Convert to polar form (r, theta), such that self = r * exp(i * theta)

pub fn from_polar(r: T, theta: T) -> Self

Convert a polar representation into a complex number.

pub fn exp(self) -> Self

Computes e^(self), where e is the base of the natural logarithm.

pub fn ln(self) -> Self

Computes the principal value of natural logarithm of self.

This function has one branch cut:

• (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

pub fn sqrt(self) -> Self

Computes the principal value of the square root of self.

This function has one branch cut:

• (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

pub fn cbrt(self) -> Self

Computes the principal value of the cube root of self.

This function has one branch cut:

• (-∞, 0), continuous from above.

The branch satisfies -π/3 ≤ arg(cbrt(z)) ≤ π/3.

Note that this does not match the usual result for the cube root of negative real numbers. For example, the real cube root of -8 is -2, but the principal complex cube root of -8 is 1 + i√3.

pub fn powf(self, exp: T) -> Self

Raises self to a floating point power.

pub fn log(self, base: T) -> Self

Returns the logarithm of self with respect to an arbitrary base.

pub fn powc(self, exp: Self) -> Self

Raises self to a complex power.

pub fn expf(self, base: T) -> Self

Raises a floating point number to the complex power self.

pub fn sin(self) -> Self

Computes the sine of self.

pub fn cos(self) -> Self

Computes the cosine of self.

pub fn tan(self) -> Self

Computes the tangent of self.

pub fn asin(self) -> Self

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

pub fn acos(self) -> Self

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

pub fn atan(self) -> Self

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

• (-∞i, -i], continuous from the left.
• [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

pub fn sinh(self) -> Self

Computes the hyperbolic sine of self.

pub fn cosh(self) -> Self

Computes the hyperbolic cosine of self.

pub fn tanh(self) -> Self

Computes the hyperbolic tangent of self.

pub fn asinh(self) -> Self

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

• (-∞i, -i), continuous from the left.
• (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

pub fn acosh(self) -> Self

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

• (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

pub fn atanh(self) -> Self

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

• (-∞, -1], continuous from above.
• [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

pub fn finv(self) -> Complex<T>

Returns 1/self using floating-point operations.

This may be more accurate than the generic self.inv() in cases where self.norm_sqr() would overflow to ∞ or underflow to 0.

Examples

use num_complex::Complex64;
let c = Complex64::new(1e300, 1e300);

// The generic `inv()` will overflow.
assert!(!c.inv().is_normal());

// But we can do better for `Float` types.
let inv = c.finv();
assert!(inv.is_normal());
println!("{:e}", inv);

let expected = Complex64::new(5e-301, -5e-301);
assert!((inv - expected).norm() < 1e-315);

pub fn fdiv(self, other: Complex<T>) -> Complex<T>

Returns self/other using floating-point operations.

This may be more accurate than the generic Div implementation in cases where other.norm_sqr() would overflow to ∞ or underflow to 0.

Examples

use num_complex::Complex64;
let a = Complex64::new(2.0, 3.0);
let b = Complex64::new(1e300, 1e300);

// Generic division will overflow.
assert!(!(a / b).is_normal());

// But we can do better for `Float` types.
let quotient = a.fdiv(b);
assert!(quotient.is_normal());
println!("{:e}", quotient);

let expected = Complex64::new(2.5e-300, 5e-301);
assert!((quotient - expected).norm() < 1e-315);

impl<T: Float + FloatConst> Complex<T>

pub fn exp2(self) -> Self

Computes 2^(self).

pub fn log2(self) -> Self

Computes the principal value of log base 2 of self.

pub fn log10(self) -> Self

Computes the principal value of log base 10 of self.

impl<T: FloatCore> Complex<T>

pub fn is_nan(self) -> bool

Checks if the given complex number is NaN

pub fn is_infinite(self) -> bool

Checks if the given complex number is infinite

pub fn is_finite(self) -> bool

Checks if the given complex number is finite

pub fn is_normal(self) -> bool

Checks if the given complex number is normal

impl<T: ConstZero> Complex<T>

pub const ZERO: Self = _

A constant Complex 0.

impl<T: ConstOne + ConstZero> Complex<T>

pub const ONE: Self = _

A constant Complex 1.

pub const I: Self = _

A constant Complex i, the imaginary unit.

Trait Implementations

impl<'a, 'b, T: Clone + Num> Add<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &Complex<T>) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &Complex<T>) -> Self::Output

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f32>) -> Complex<f32>

Performs the + operation.

impl<'a> Add<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f32>) -> Complex<f32>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f64>) -> Complex<f64>

Performs the + operation.

impl<'a> Add<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f64>) -> Complex<f64>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i128>) -> Complex<i128>

Performs the + operation.

impl<'a> Add<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i128>) -> Complex<i128>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i16>) -> Complex<i16>

Performs the + operation.

impl<'a> Add<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i16>) -> Complex<i16>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i32>) -> Complex<i32>

Performs the + operation.

impl<'a> Add<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i32>) -> Complex<i32>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i64>) -> Complex<i64>

Performs the + operation.

impl<'a> Add<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i64>) -> Complex<i64>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i8>) -> Complex<i8>

Performs the + operation.

impl<'a> Add<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i8>) -> Complex<i8>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<isize>) -> Complex<isize>

Performs the + operation.

impl<'a> Add<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<isize>) -> Complex<isize>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u128>) -> Complex<u128>

Performs the + operation.

impl<'a> Add<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u128>) -> Complex<u128>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u16>) -> Complex<u16>

Performs the + operation.

impl<'a> Add<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u16>) -> Complex<u16>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u32>) -> Complex<u32>

Performs the + operation.

impl<'a> Add<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u32>) -> Complex<u32>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u64>) -> Complex<u64>

Performs the + operation.

impl<'a> Add<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u64>) -> Complex<u64>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u8>) -> Complex<u8>

Performs the + operation.

impl<'a> Add<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u8>) -> Complex<u8>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<usize>) -> Complex<usize>

Performs the + operation.

impl<'a> Add<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<usize>) -> Complex<usize>

Performs the + operation.

impl<'a, 'b, T: Clone + Num> Add<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &T) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &T) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: Complex<T>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: Complex<f32>) -> Complex<f32>

Performs the + operation.

impl Add<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: Complex<f32>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: Complex<f64>) -> Complex<f64>

Performs the + operation.

impl Add<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: Complex<f64>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: Complex<i128>) -> Complex<i128>

Performs the + operation.

impl Add<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: Complex<i128>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: Complex<i16>) -> Complex<i16>

Performs the + operation.

impl Add<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: Complex<i16>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: Complex<i32>) -> Complex<i32>

Performs the + operation.

impl Add<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: Complex<i32>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: Complex<i64>) -> Complex<i64>

Performs the + operation.

impl Add<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: Complex<i64>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: Complex<i8>) -> Complex<i8>

Performs the + operation.

impl Add<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: Complex<i8>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: Complex<isize>) -> Complex<isize>

Performs the + operation.

impl Add<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: Complex<isize>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: Complex<u128>) -> Complex<u128>

Performs the + operation.

impl Add<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: Complex<u128>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: Complex<u16>) -> Complex<u16>

Performs the + operation.

impl Add<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: Complex<u16>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: Complex<u32>) -> Complex<u32>

Performs the + operation.

impl Add<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: Complex<u32>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: Complex<u64>) -> Complex<u64>

Performs the + operation.

impl Add<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: Complex<u64>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: Complex<u8>) -> Complex<u8>

Performs the + operation.

impl Add<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: Complex<u8>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: Complex<usize>) -> Complex<usize>

Performs the + operation.

impl Add<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: Complex<usize>) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: T) -> Self::Output

Performs the + operation.

impl<T: Clone + Num> Add<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: T) -> Self::Output

Performs the + operation.

impl<T: Clone + Num> Add for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: Self) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + NumAssign> AddAssign<&'a Complex<T>> for Complex<T>

fn add_assign(&mut self, other: &Self)

Performs the += operation.

impl<'a, T: Clone + NumAssign> AddAssign<&'a T> for Complex<T>

fn add_assign(&mut self, other: &T)

Performs the += operation.

impl<T: Clone + NumAssign> AddAssign<T> for Complex<T>

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<T: Clone + NumAssign> AddAssign for Complex<T>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<T> Archive for Complex<T>

where T: Archive,

type Archived = Complex<<T as Archive>::Archived>

The archived representation of this type.

type Resolver = ComplexResolver<T>

The resolver for this type. It must contain all the additional information from serializing needed to make the archived type from the normal type.

unsafe fn resolve( &self, pos: usize, resolver: Self::Resolver, out: *mut Self::Archived )

Creates the archived version of this value at the given position and writes it to the given output.

impl<T, U> AsPrimitive<U> for Complex<T>

where T: AsPrimitive<U>, U: 'static + Copy,

fn as_(self) -> U

Convert a value to another, using the as operator.

impl<T> Binary for Complex<T>

where T: Binary + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<__C: ?Sized, T> CheckBytes<__C> for Complex<T>

where T: CheckBytes<__C>,

type Error = StructCheckError

The error that may result from checking the type.

unsafe fn check_bytes<'__bytecheck>( value: *const Self, context: &mut __C ) -> Result<&'__bytecheck Self, StructCheckError>

Checks whether the given pointer points to a valid value within the given context.

impl<T: Clone> Clone for Complex<T>

fn clone(&self) -> Complex<T>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Float + FloatConst> ComplexFloat for Complex<T>

type Real = T

The type used to represent the real coefficients of this complex number.

fn re(self) -> Self::Real

Returns the real part of the number.

fn im(self) -> Self::Real

Returns the imaginary part of the number.

fn abs(self) -> Self::Real

Returns the absolute value of the number. See also Complex::norm

fn recip(self) -> Self

Take the reciprocal (inverse) of a number, 1/x. See also Complex::finv.

fn l1_norm(&self) -> Self::Real

Returns the L1 norm |re| + |im| – the Manhattan distance from the origin.

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN.

fn arg(self) -> Self::Real

Computes the argument of the number.

fn powc(self, exp: Complex<Self::Real>) -> Complex<Self::Real>

Raises self to a complex power.

fn exp2(self) -> Self

Returns 2^(self).

fn log(self, base: Self::Real) -> Self

Returns the logarithm of the number with respect to an arbitrary base.

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

fn powf(self, f: Self::Real) -> Self

Raises self to a real power.

fn sqrt(self) -> Self

Take the square root of a number.

fn cbrt(self) -> Self

Take the cubic root of a number.

fn exp(self) -> Self

Returns e^(self), (the exponential function).

fn expf(self, base: Self::Real) -> Self

Returns base^(self).

fn ln(self) -> Self

Returns the natural logarithm of the number.

fn sin(self) -> Self

Computes the sine of a number (in radians).

fn cos(self) -> Self

Computes the cosine of a number (in radians).

fn tan(self) -> Self

Computes the tangent of a number (in radians).

fn asin(self) -> Self

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

fn acos(self) -> Self

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

fn sinh(self) -> Self

Hyperbolic sine function.

fn cosh(self) -> Self

Hyperbolic cosine function.

fn tanh(self) -> Self

Hyperbolic tangent function.

fn asinh(self) -> Self

Inverse hyperbolic sine function.

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

fn powi(self, n: i32) -> Self

Raises self to a signed integer power.

fn conj(self) -> Self

Computes the complex conjugate of the number.

impl<T: Clone + Num + ConstOne + ConstZero> ConstOne for Complex<T>

const ONE: Self = Self::ONE

The multiplicative identity element of Self, 1.

impl<T: Clone + Num + ConstZero> ConstZero for Complex<T>

const ZERO: Self = Self::ZERO

The additive identity element of Self, 0.

impl<T: Debug> Debug for Complex<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Default> Default for Complex<T>

fn default() -> Complex<T>

Returns the “default value” for a type.

impl<'de, T> Deserialize<'de> for Complex<T>

where T: Deserialize<'de>,

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<__D: Fallible + ?Sized, T> Deserialize<Complex<T>, __D> for Archived<Complex<T>>

where T: Archive, Archived<T>: Deserialize<T, __D>,

fn deserialize(&self, deserializer: &mut __D) -> Result<Complex<T>, __D::Error>

Deserializes using the given deserializer

impl<T> Display for Complex<T>

where T: Display + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T, Re, Im> Distribution<Complex<T>> for ComplexDistribution<Re, Im>

where T: Num + Clone, Re: Distribution<T>, Im: Distribution<T>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Complex<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T> Distribution<Complex<T>> for Standard

where T: Num + Clone, Standard: Distribution<T>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Complex<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<'a, 'b, T: Clone + Num> Div<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &Complex<T>) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &Complex<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f32>) -> Complex<f32>

Performs the / operation.

impl<'a> Div<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f32>) -> Complex<f32>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f64>) -> Complex<f64>

Performs the / operation.

impl<'a> Div<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f64>) -> Complex<f64>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i128>) -> Complex<i128>

Performs the / operation.

impl<'a> Div<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i128>) -> Complex<i128>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i16>) -> Complex<i16>

Performs the / operation.

impl<'a> Div<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i16>) -> Complex<i16>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i32>) -> Complex<i32>

Performs the / operation.

impl<'a> Div<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i32>) -> Complex<i32>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i64>) -> Complex<i64>

Performs the / operation.

impl<'a> Div<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i64>) -> Complex<i64>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i8>) -> Complex<i8>

Performs the / operation.

impl<'a> Div<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i8>) -> Complex<i8>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<isize>) -> Complex<isize>

Performs the / operation.

impl<'a> Div<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<isize>) -> Complex<isize>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u128>) -> Complex<u128>

Performs the / operation.

impl<'a> Div<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u128>) -> Complex<u128>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u16>) -> Complex<u16>

Performs the / operation.

impl<'a> Div<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u16>) -> Complex<u16>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u32>) -> Complex<u32>

Performs the / operation.

impl<'a> Div<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u32>) -> Complex<u32>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u64>) -> Complex<u64>

Performs the / operation.

impl<'a> Div<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u64>) -> Complex<u64>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u8>) -> Complex<u8>

Performs the / operation.

impl<'a> Div<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u8>) -> Complex<u8>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<usize>) -> Complex<usize>

Performs the / operation.

impl<'a> Div<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<usize>) -> Complex<usize>

Performs the / operation.

impl<'a, 'b, T: Clone + Num> Div<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &T) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &T) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: Complex<T>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: Complex<f32>) -> Complex<f32>

Performs the / operation.

impl Div<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: Complex<f32>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: Complex<f64>) -> Complex<f64>

Performs the / operation.

impl Div<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: Complex<f64>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: Complex<i128>) -> Complex<i128>

Performs the / operation.

impl Div<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: Complex<i128>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: Complex<i16>) -> Complex<i16>

Performs the / operation.

impl Div<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: Complex<i16>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: Complex<i32>) -> Complex<i32>

Performs the / operation.

impl Div<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: Complex<i32>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: Complex<i64>) -> Complex<i64>

Performs the / operation.

impl Div<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: Complex<i64>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: Complex<i8>) -> Complex<i8>

Performs the / operation.

impl Div<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: Complex<i8>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: Complex<isize>) -> Complex<isize>

Performs the / operation.

impl Div<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: Complex<isize>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: Complex<u128>) -> Complex<u128>

Performs the / operation.

impl Div<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: Complex<u128>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: Complex<u16>) -> Complex<u16>

Performs the / operation.

impl Div<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: Complex<u16>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: Complex<u32>) -> Complex<u32>

Performs the / operation.

impl Div<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: Complex<u32>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: Complex<u64>) -> Complex<u64>

Performs the / operation.

impl Div<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: Complex<u64>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: Complex<u8>) -> Complex<u8>

Performs the / operation.

impl Div<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: Complex<u8>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: Complex<usize>) -> Complex<usize>

Performs the / operation.

impl Div<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: Complex<usize>) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: T) -> Self::Output

Performs the / operation.

impl<T: Clone + Num> Div<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: T) -> Self::Output

Performs the / operation.

impl<T: Clone + Num> Div for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: Self) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + NumAssign> DivAssign<&'a Complex<T>> for Complex<T>

fn div_assign(&mut self, other: &Self)

Performs the /= operation.

impl<'a, T: Clone + NumAssign> DivAssign<&'a T> for Complex<T>

fn div_assign(&mut self, other: &T)

Performs the /= operation.

impl<T: Clone + NumAssign> DivAssign<T> for Complex<T>

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<T: Clone + NumAssign> DivAssign for Complex<T>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<'a, T: Clone + Num> From<&'a T> for Complex<T>

fn from(re: &T) -> Self

Converts to this type from the input type.

impl<T: Clone + Num> From<T> for Complex<T>

fn from(re: T) -> Self

Converts to this type from the input type.

impl<T: FromPrimitive + Num> FromPrimitive for Complex<T>

fn from_usize(n: usize) -> Option<Self>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_isize(n: isize) -> Option<Self>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u8(n: u8) -> Option<Self>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u16(n: u16) -> Option<Self>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u32(n: u32) -> Option<Self>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u64(n: u64) -> Option<Self>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i8(n: i8) -> Option<Self>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i16(n: i16) -> Option<Self>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i32(n: i32) -> Option<Self>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i64(n: i64) -> Option<Self>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u128(n: u128) -> Option<Self>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i128(n: i128) -> Option<Self>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f32(n: f32) -> Option<Self>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f64(n: f64) -> Option<Self>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

impl<T> FromStr for Complex<T>

where T: FromStr + Num + Clone,

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

type Err = ParseComplexError<<T as FromStr>::Err>

The associated error which can be returned from parsing.

impl<T: Hash> Hash for Complex<T>

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<'a, T: Clone + Num + Neg<Output = T>> Inv for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T: Clone + Num + Neg<Output = T>> Inv for Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T> LowerExp for Complex<T>

where T: LowerExp + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T> LowerHex for Complex<T>

where T: LowerHex + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a, 'b, T: Clone + Num> Mul<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f32>) -> Complex<f32>

Performs the * operation.

impl<'a> Mul<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f32>) -> Complex<f32>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f64>) -> Complex<f64>

Performs the * operation.

impl<'a> Mul<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f64>) -> Complex<f64>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i128>) -> Complex<i128>

Performs the * operation.

impl<'a> Mul<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i128>) -> Complex<i128>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i16>) -> Complex<i16>

Performs the * operation.

impl<'a> Mul<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i16>) -> Complex<i16>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i32>) -> Complex<i32>

Performs the * operation.

impl<'a> Mul<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i32>) -> Complex<i32>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i64>) -> Complex<i64>

Performs the * operation.

impl<'a> Mul<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i64>) -> Complex<i64>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i8>) -> Complex<i8>

Performs the * operation.

impl<'a> Mul<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i8>) -> Complex<i8>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<isize>) -> Complex<isize>

Performs the * operation.

impl<'a> Mul<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<isize>) -> Complex<isize>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u128>) -> Complex<u128>

Performs the * operation.

impl<'a> Mul<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u128>) -> Complex<u128>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u16>) -> Complex<u16>

Performs the * operation.

impl<'a> Mul<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u16>) -> Complex<u16>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u32>) -> Complex<u32>

Performs the * operation.

impl<'a> Mul<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u32>) -> Complex<u32>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u64>) -> Complex<u64>

Performs the * operation.

impl<'a> Mul<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u64>) -> Complex<u64>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u8>) -> Complex<u8>

Performs the * operation.

impl<'a> Mul<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u8>) -> Complex<u8>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<usize>) -> Complex<usize>

Performs the * operation.

impl<'a> Mul<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<usize>) -> Complex<usize>

Performs the * operation.

impl<'a, 'b, T: Clone + Num> Mul<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &T) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &T) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: Complex<T>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f32>) -> Complex<f32>

Performs the * operation.

impl Mul<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f32>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f64>) -> Complex<f64>

Performs the * operation.

impl Mul<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f64>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i128>) -> Complex<i128>

Performs the * operation.

impl Mul<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i128>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i16>) -> Complex<i16>

Performs the * operation.

impl Mul<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i16>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i32>) -> Complex<i32>

Performs the * operation.

impl Mul<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i32>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i64>) -> Complex<i64>

Performs the * operation.

impl Mul<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i64>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i8>) -> Complex<i8>

Performs the * operation.

impl Mul<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i8>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<isize>) -> Complex<isize>

Performs the * operation.

impl Mul<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<isize>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u128>) -> Complex<u128>

Performs the * operation.

impl Mul<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u128>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u16>) -> Complex<u16>

Performs the * operation.

impl Mul<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u16>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u32>) -> Complex<u32>

Performs the * operation.

impl Mul<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u32>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u64>) -> Complex<u64>

Performs the * operation.

impl Mul<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u64>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u8>) -> Complex<u8>

Performs the * operation.

impl Mul<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u8>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<usize>) -> Complex<usize>

Performs the * operation.

impl Mul<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<usize>) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self::Output

Performs the * operation.

impl<T: Clone + Num> Mul<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self::Output

Performs the * operation.

impl<T: Clone + Num> Mul for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: Self) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: Clone + Num + MulAdd<Output = T>> MulAdd<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

fn mul_add(self, other: &Complex<T>, add: &Complex<T>) -> Complex<T>

Performs the fused multiply-add operation (self * a) + b

impl<T: Clone + Num + MulAdd<Output = T>> MulAdd for Complex<T>

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

fn mul_add(self, other: Complex<T>, add: Complex<T>) -> Complex<T>

Performs the fused multiply-add operation (self * a) + b

impl<'a, 'b, T: Clone + NumAssign + MulAddAssign> MulAddAssign<&'a Complex<T>, &'b Complex<T>> for Complex<T>

fn mul_add_assign(&mut self, other: &Complex<T>, add: &Complex<T>)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<T: Clone + NumAssign + MulAddAssign> MulAddAssign for Complex<T>

fn mul_add_assign(&mut self, other: Complex<T>, add: Complex<T>)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<'a, T: Clone + NumAssign> MulAssign<&'a Complex<T>> for Complex<T>

fn mul_assign(&mut self, other: &Self)

Performs the *= operation.

impl<'a, T: Clone + NumAssign> MulAssign<&'a T> for Complex<T>

fn mul_assign(&mut self, other: &T)

Performs the *= operation.

impl<T: Clone + NumAssign> MulAssign<T> for Complex<T>

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<T: Clone + NumAssign> MulAssign for Complex<T>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<'a, T: Clone + Num + Neg<Output = T>> Neg for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: Clone + Num + Neg<Output = T>> Neg for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: Num + Clone> Num for Complex<T>

fn from_str_radix(s: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

radix must be <= 18; larger radix would include i and j as digits, which cannot be supported.

The conversion returns an error if 18 <= radix <= 36; it panics if radix > 36.

The elements of T are parsed using Num::from_str_radix too, and errors (or panics) from that are reflected here as well.

type FromStrRadixErr = ParseComplexError<<T as Num>::FromStrRadixErr>

impl<T: NumCast + Num> NumCast for Complex<T>

fn from<U: ToPrimitive>(n: U) -> Option<Self>

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned.

impl<T> Octal for Complex<T>

where T: Octal + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Clone + Num> One for Complex<T>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl<T: PartialEq> PartialEq for Complex<T>

fn eq(&self, other: &Complex<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, 'b, T: Float> Pow<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &'b Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<'b, T: Float> Pow<&'b Complex<T>> for Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &'b Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Float> Pow<&'b f32> for &'a Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f32) -> Self::Output

Returns self to the power rhs.

impl<'b, T: Float> Pow<&'b f32> for Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f32) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Float> Pow<&'b f64> for &'a Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f64) -> Self::Output

Returns self to the power rhs.

impl<'b, T: Float> Pow<&'b f64> for Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f64) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i128) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i16) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i32) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i64) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i8) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b isize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &isize) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u128) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u16) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u32) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u64) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u8) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b usize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &usize) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Float> Pow<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<T: Float> Pow<Complex<T>> for Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Float> Pow<f32> for &'a Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f32) -> Self::Output

Returns self to the power rhs.

impl<T: Float> Pow<f32> for Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f32) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Float> Pow<f64> for &'a Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f64) -> Self::Output

Returns self to the power rhs.

impl<T: Float> Pow<f64> for Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f64) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i128) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i16) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i32) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i64) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i8) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<isize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: isize) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u128) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u16) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u32) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u64) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u8) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<usize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: usize) -> Self::Output

Returns self to the power rhs.

impl<'a, T: 'a + Num + Clone> Product<&'a Complex<T>> for Complex<T>

fn product<I>(iter: I) -> Self

where I: Iterator<Item = &'a Complex<T>>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<T: Num + Clone> Product for Complex<T>

fn product<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<'a, 'b, T: Clone + Num> Rem<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<T>) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<T>) -> Self::Output

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f32>) -> Complex<f32>

Performs the % operation.

impl<'a> Rem<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f32>) -> Complex<f32>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f64>) -> Complex<f64>

Performs the % operation.

impl<'a> Rem<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f64>) -> Complex<f64>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i128>) -> Complex<i128>

Performs the % operation.

impl<'a> Rem<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i128>) -> Complex<i128>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i16>) -> Complex<i16>

Performs the % operation.

impl<'a> Rem<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i16>) -> Complex<i16>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i32>) -> Complex<i32>

Performs the % operation.

impl<'a> Rem<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i32>) -> Complex<i32>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i64>) -> Complex<i64>

Performs the % operation.

impl<'a> Rem<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i64>) -> Complex<i64>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i8>) -> Complex<i8>

Performs the % operation.

impl<'a> Rem<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i8>) -> Complex<i8>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<isize>) -> Complex<isize>

Performs the % operation.

impl<'a> Rem<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<isize>) -> Complex<isize>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u128>) -> Complex<u128>

Performs the % operation.

impl<'a> Rem<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u128>) -> Complex<u128>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u16>) -> Complex<u16>

Performs the % operation.

impl<'a> Rem<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u16>) -> Complex<u16>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u32>) -> Complex<u32>

Performs the % operation.

impl<'a> Rem<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u32>) -> Complex<u32>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u64>) -> Complex<u64>

Performs the % operation.

impl<'a> Rem<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u64>) -> Complex<u64>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u8>) -> Complex<u8>

Performs the % operation.

impl<'a> Rem<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u8>) -> Complex<u8>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<usize>) -> Complex<usize>

Performs the % operation.

impl<'a> Rem<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<usize>) -> Complex<usize>

Performs the % operation.

impl<'a, 'b, T: Clone + Num> Rem<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &T) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &T) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: Complex<T>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f32>) -> Complex<f32>

Performs the % operation.

impl Rem<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f32>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f64>) -> Complex<f64>

Performs the % operation.

impl Rem<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f64>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i128>) -> Complex<i128>

Performs the % operation.

impl Rem<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i128>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i16>) -> Complex<i16>

Performs the % operation.

impl Rem<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i16>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i32>) -> Complex<i32>

Performs the % operation.

impl Rem<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i32>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i64>) -> Complex<i64>

Performs the % operation.

impl Rem<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i64>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i8>) -> Complex<i8>

Performs the % operation.

impl Rem<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i8>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<isize>) -> Complex<isize>

Performs the % operation.

impl Rem<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<isize>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u128>) -> Complex<u128>

Performs the % operation.

impl Rem<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u128>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u16>) -> Complex<u16>

Performs the % operation.

impl Rem<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u16>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u32>) -> Complex<u32>

Performs the % operation.

impl Rem<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u32>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u64>) -> Complex<u64>

Performs the % operation.

impl Rem<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u64>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u8>) -> Complex<u8>

Performs the % operation.

impl Rem<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u8>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<usize>) -> Complex<usize>

Performs the % operation.

impl Rem<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<usize>) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: T) -> Self::Output

Performs the % operation.

impl<T: Clone + Num> Rem<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: T) -> Self::Output

Performs the % operation.

impl<T: Clone + Num> Rem for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, modulus: Self) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + NumAssign> RemAssign<&'a Complex<T>> for Complex<T>

fn rem_assign(&mut self, other: &Self)

Performs the %= operation.

impl<'a, T: Clone + NumAssign> RemAssign<&'a T> for Complex<T>

fn rem_assign(&mut self, other: &T)

Performs the %= operation.

impl<T: Clone + NumAssign> RemAssign<T> for Complex<T>

fn rem_assign(&mut self, other: T)

Performs the %= operation.

impl<T: Clone + NumAssign> RemAssign for Complex<T>

fn rem_assign(&mut self, modulus: Self)

Performs the %= operation.

impl<__S: Fallible + ?Sized, T> Serialize<__S> for Complex<T>

where T: Serialize<__S>,

fn serialize(&self, serializer: &mut __S) -> Result<Self::Resolver, __S::Error>

Writes the dependencies for the object and returns a resolver that can create the archived type.

impl<T> Serialize for Complex<T>

where T: Serialize,

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<'a, 'b, T: Clone + Num> Sub<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<T>) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + Num> Sub<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<T>) -> Self::Output

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f32>) -> Complex<f32>

Performs the - operation.

impl<'a> Sub<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f32>) -> Complex<f32>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f64>) -> Complex<f64>

Performs the - operation.

impl<'a> Sub<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f64>) -> Complex<f64>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i128>) -> Complex<i128>

Performs the - operation.

impl<'a> Sub<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i128>) -> Complex<i128>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i16>) -> Complex<i16>

Performs the - operation.

impl<'a> Sub<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i16>) -> Complex<i16>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i32>) -> Complex<i32>

Performs the - operation.

impl<'a> Sub<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i32>) -> Complex<i32>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i64>) -> Complex<i64>

Performs the - operation.

impl<'a> Sub<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i64>) -> Complex<i64>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i8>) -> Complex<i8>

Performs the - operation.

impl<'a> Sub<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i8>) -> Complex<i8>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<isize>) -> Complex<isize>

Performs the - operation.

impl<'a> Sub<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<isize>) -> Complex<isize>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u128>) -> Complex<u128>

Performs the - operation.

impl<'a> Sub<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u128>) -> Complex<u128>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u16>) -> Complex<u16>

Performs the - operation.

impl<'a> Sub<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u16>) -> Complex<u16>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u32>) -> Complex<u32>

Performs the - operation.

impl<'a> Sub<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u32>) -> Complex<u32>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u64>) -> Complex<u64>

Performs the - operation.

impl<'a> Sub<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u64>) -> Complex<u64>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u8>) -> Complex<u8>

Performs the - operation.

impl<'a> Sub<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u8>) -> Complex<u8>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<usize>) -> Complex<usize>

Performs the - operation.

impl<'a> Sub<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<usize>) -> Complex<usize>

Performs the - operation.

impl<'a, 'b, T: Clone + Num> Sub<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &T) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + Num> Sub<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &T) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + Num> Sub<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: Complex<T>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f32>) -> Complex<f32>

Performs the - operation.

impl Sub<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f32>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f64>) -> Complex<f64>

Performs the - operation.

impl Sub<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f64>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i128>) -> Complex<i128>

Performs the - operation.

impl Sub<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i128>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i16>) -> Complex<i16>

Performs the - operation.

impl Sub<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i16>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i32>) -> Complex<i32>

Performs the - operation.

impl Sub<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i32>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i64>) -> Complex<i64>

Performs the - operation.

impl Sub<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i64>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i8>) -> Complex<i8>

Performs the - operation.

impl Sub<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i8>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the - operator.

fn sub(self, other: Complex<isize>) -> Complex<isize>

Performs the - operation.

impl Sub<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the - operator.

fn sub(self, other: Complex<isize>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u128>) -> Complex<u128>

Performs the - operation.

impl Sub<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u128>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u16>) -> Complex<u16>

Performs the - operation.

impl Sub<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u16>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u32>) -> Complex<u32>

Performs the - operation.

impl Sub<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u32>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u64>) -> Complex<u64>

Performs the - operation.

impl Sub<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u64>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u8>) -> Complex<u8>

Performs the - operation.

impl Sub<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the - operator.

fn sub(self, other: Complex<u8>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the - operator.

fn sub(self, other: Complex<usize>) -> Complex<usize>

Performs the - operation.

impl Sub<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the - operator.

fn sub(self, other: Complex<usize>) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + Num> Sub<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: T) -> Self::Output

Performs the - operation.

impl<T: Clone + Num> Sub<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: T) -> Self::Output

Performs the - operation.

impl<T: Clone + Num> Sub for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: Self) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + NumAssign> SubAssign<&'a Complex<T>> for Complex<T>

fn sub_assign(&mut self, other: &Self)

Performs the -= operation.

impl<'a, T: Clone + NumAssign> SubAssign<&'a T> for Complex<T>

fn sub_assign(&mut self, other: &T)

Performs the -= operation.

impl<T: Clone + NumAssign> SubAssign<T> for Complex<T>

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<T: Clone + NumAssign> SubAssign for Complex<T>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, T: 'a + Num + Clone> Sum<&'a Complex<T>> for Complex<T>

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = &'a Complex<T>>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<T: Num + Clone> Sum for Complex<T>

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<T: ToPrimitive + Num> ToPrimitive for Complex<T>

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

impl<T> UpperExp for Complex<T>

where T: UpperExp + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T> UpperHex for Complex<T>

where T: UpperHex + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Clone + Num> Zero for Complex<T>

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<T: Zeroable> Zeroable for Complex<T>

fn zeroed() -> Self

Calls zeroed.

impl<T: Copy> Copy for Complex<T>

impl<T: Eq> Eq for Complex<T>

impl<T: Pod> Pod for Complex<T>

impl<T> StructuralPartialEq for Complex<T>