/Go

# Package cmplx

## Overview

Package cmplx provides basic constants and mathematical functions for complex numbers.

Abs
Exp
Polar

## func AbsSource

`func Abs(x complex128) float64`

Abs returns the absolute value (also called the modulus) of x.

#### Example

```package main

import (
"fmt"
"math/cmplx"
)

func main() {
fmt.Printf("%.1f", cmplx.Abs(3+4i))
}
```

## func AcosSource

`func Acos(x complex128) complex128`

Acos returns the inverse cosine of x.

## func AcoshSource

`func Acosh(x complex128) complex128`

Acosh returns the inverse hyperbolic cosine of x.

## func AsinSource

`func Asin(x complex128) complex128`

Asin returns the inverse sine of x.

## func AsinhSource

`func Asinh(x complex128) complex128`

Asinh returns the inverse hyperbolic sine of x.

## func AtanSource

`func Atan(x complex128) complex128`

Atan returns the inverse tangent of x.

## func AtanhSource

`func Atanh(x complex128) complex128`

Atanh returns the inverse hyperbolic tangent of x.

## func ConjSource

`func Conj(x complex128) complex128`

Conj returns the complex conjugate of x.

## func CosSource

`func Cos(x complex128) complex128`

Cos returns the cosine of x.

## func CoshSource

`func Cosh(x complex128) complex128`

Cosh returns the hyperbolic cosine of x.

## func CotSource

`func Cot(x complex128) complex128`

Cot returns the cotangent of x.

## func ExpSource

`func Exp(x complex128) complex128`

Exp returns e**x, the base-e exponential of x.

#### Example

ExampleExp computes Euler's identity.

```package main

import (
"fmt"
"math"
"math/cmplx"
)

func main() {
fmt.Printf("%.1f", cmplx.Exp(1i*math.Pi)+1)
}
```

## func InfSource

`func Inf() complex128`

Inf returns a complex infinity, complex(+Inf, +Inf).

## func IsInfSource

`func IsInf(x complex128) bool`

IsInf returns true if either real(x) or imag(x) is an infinity.

## func IsNaNSource

`func IsNaN(x complex128) bool`

IsNaN returns true if either real(x) or imag(x) is NaN and neither is an infinity.

## func LogSource

`func Log(x complex128) complex128`

Log returns the natural logarithm of x.

## func Log10Source

`func Log10(x complex128) complex128`

Log10 returns the decimal logarithm of x.

## func NaNSource

`func NaN() complex128`

NaN returns a complex “not-a-number” value.

## func PhaseSource

`func Phase(x complex128) float64`

Phase returns the phase (also called the argument) of x. The returned value is in the range [-Pi, Pi].

## func PolarSource

`func Polar(x complex128) (r, θ float64)`

Polar returns the absolute value r and phase θ of x, such that x = r * e**θi. The phase is in the range [-Pi, Pi].

#### Example

```package main

import (
"fmt"
"math"
"math/cmplx"
)

func main() {
r, theta := cmplx.Polar(2i)
fmt.Printf("r: %.1f, θ: %.1f*π", r, theta/math.Pi)
}
```

## func PowSource

`func Pow(x, y complex128) complex128`

Pow returns x**y, the base-x exponential of y. For generalized compatibility with math.Pow:

```Pow(0, ±0) returns 1+0i
Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
```

## func RectSource

`func Rect(r, θ float64) complex128`

Rect returns the complex number x with polar coordinates r, θ.

## func SinSource

`func Sin(x complex128) complex128`

Sin returns the sine of x.

## func SinhSource

`func Sinh(x complex128) complex128`

Sinh returns the hyperbolic sine of x.

## func SqrtSource

`func Sqrt(x complex128) complex128`

Sqrt returns the square root of x. The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).

## func TanSource

`func Tan(x complex128) complex128`

Tan returns the tangent of x.

## func TanhSource

`func Tanh(x complex128) complex128`

Tanh returns the hyperbolic tangent of x.