Struct Complex 

pub struct Complex {
    pub re: f64,
    pub im: f64,
}

A complex number z = re + i·im.

Fields

re: f64

Real part.

im: f64

Imaginary part.

Implementations

impl Complex

pub fn new(re: f64, im: f64) -> Self

Construct a new complex number.

pub fn from_real(re: f64) -> Self

The purely real number re + 0i.

pub fn from_imag(im: f64) -> Self

The purely imaginary number 0 + im·i.

pub fn zero() -> Self

The additive identity 0.

pub fn one() -> Self

The multiplicative identity 1.

pub fn i() -> Self

The imaginary unit i.

pub fn abs(&self) -> f64

Absolute value (modulus) |z| = sqrt(re² + im²).

pub fn arg(&self) -> f64

Argument (phase angle) arg(z) = atan2(im, re) in radians.

pub fn conj(&self) -> Self

Complex conjugate z̄ = re − i·im.

pub fn norm_sq(&self) -> f64

Squared modulus |z|².

pub fn inv(&self) -> Self

Multiplicative inverse 1/z.

Returns NaN-valued complex if z == 0.

pub fn exp(&self) -> Self

Complex exponential e^z = e^re · (cos(im) + i·sin(im)).

pub fn ln(&self) -> Self

Principal natural logarithm ln(z) = ln|z| + i·arg(z).

pub fn sqrt(&self) -> Self

Principal square root √z.

pub fn pow(&self, n: f64) -> Self

Raise to a real power: z^n = |z|^n · e^(i·n·arg(z)).

pub fn cpow(&self, w: Self) -> Self

Raise to a complex power: z^w = e^(w · ln z).

pub fn sin(&self) -> Self

Complex sine sin(z) = sin(re)·cosh(im) + i·cos(re)·sinh(im).

pub fn cos(&self) -> Self

Complex cosine cos(z) = cos(re)·cosh(im) − i·sin(re)·sinh(im).

pub fn sinh(&self) -> Self

Complex hyperbolic sine sinh(z) = sinh(re)·cos(im) + i·cosh(re)·sin(im).

pub fn cosh(&self) -> Self

Complex hyperbolic cosine cosh(z) = cosh(re)·cos(im) + i·sinh(re)·sin(im).

pub fn tan(&self) -> Self

Complex tangent tan(z) = sin(z)/cos(z).

pub fn approx_eq(&self, other: Self, tol: f64) -> bool

Test approximate equality within tolerance.

Trait Implementations

impl Add<f64> for Complex

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: f64) -> Self

Performs the + operation.

impl Add for Complex

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl Clone for Complex

fn clone(&self) -> Complex

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Complex

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

Formats the value using the given formatter.

impl Display for Complex

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

Formats the value using the given formatter.

impl Div<f64> for Complex

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: f64) -> Self

Performs the / operation.

impl Div for Complex

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self

Performs the / operation.

impl Mul<f64> for Complex

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: f64) -> Self

Performs the * operation.

impl Mul for Complex

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl Neg for Complex

type Output = Complex

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Complex

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Sub for Complex

type Output = Complex

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl Copy for Complex

impl StructuralPartialEq for Complex