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# Package cmplx

`import "math/cmplx"`
Overview
Index
Examples

## Overview ▾

Package cmplx provides basic constants and mathematical functions for complex numbers. Special case handling conforms to the C99 standard Annex G IEC 60559-compatible complex arithmetic.

## func Abs¶

`func Abs(x complex128) float64`

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

Example

```5.0
```

## func Acos¶

`func Acos(x complex128) complex128`

Acos returns the inverse cosine of x.

## func Acosh¶

`func Acosh(x complex128) complex128`

Acosh returns the inverse hyperbolic cosine of x.

## func Asin¶

`func Asin(x complex128) complex128`

Asin returns the inverse sine of x.

## func Asinh¶

`func Asinh(x complex128) complex128`

Asinh returns the inverse hyperbolic sine of x.

## func Atan¶

`func Atan(x complex128) complex128`

Atan returns the inverse tangent of x.

## func Atanh¶

`func Atanh(x complex128) complex128`

Atanh returns the inverse hyperbolic tangent of x.

## func Conj¶

`func Conj(x complex128) complex128`

Conj returns the complex conjugate of x.

## func Cos¶

`func Cos(x complex128) complex128`

Cos returns the cosine of x.

## func Cosh¶

`func Cosh(x complex128) complex128`

Cosh returns the hyperbolic cosine of x.

## func Cot¶

`func Cot(x complex128) complex128`

Cot returns the cotangent of x.

## func Exp¶

`func Exp(x complex128) complex128`

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

Example

ExampleExp computes Euler's identity.

```(0.0+0.0i)
```

## func Inf¶

`func Inf() complex128`

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

## func IsInf¶

`func IsInf(x complex128) bool`

IsInf reports whether either real(x) or imag(x) is an infinity.

## func IsNaN¶

`func IsNaN(x complex128) bool`

IsNaN reports whether either real(x) or imag(x) is NaN and neither is an infinity.

## func Log¶

`func Log(x complex128) complex128`

Log returns the natural logarithm of x.

## func Log10¶

`func Log10(x complex128) complex128`

Log10 returns the decimal logarithm of x.

## func NaN¶

`func NaN() complex128`

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

## func Phase¶

`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 Polar¶

`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

```r: 2.0, θ: 0.5*π
```

## func Pow¶

`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 Rect¶

`func Rect(r, θ float64) complex128`

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

## func Sin¶

`func Sin(x complex128) complex128`

Sin returns the sine of x.

## func Sinh¶

`func Sinh(x complex128) complex128`

Sinh returns the hyperbolic sine of x.

## func Sqrt¶

`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 Tan¶

`func Tan(x complex128) complex128`

Tan returns the tangent of x.

## func Tanh¶

`func Tanh(x complex128) complex128`

Tanh returns the hyperbolic tangent of x.