npm package: @stdlib/math-base-special-cexp
Description: Evaluate the exponential function for a double-precision complex floating-point number.
Author: The Stdlib Authors
Latest version: 0.2.3

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# exp

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Evaluate the [exponential][exponential-function] function for a double-precision complex floating-point number.

<section class="intro">

The [exponential][exponential-function] function of a complex number is defined as

<!-- <equation class="equation" label="eq:cexp_function" align="center" raw="\operatorname{exp}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))" alt="Complex exponential function"> -->

<div class="equation" align="center" data-raw-text="\operatorname{exp}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))" data-equation="eq:cexp_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d4edb68b52a6c646be5683023c5a24890300727f/lib/node_modules/@stdlib/math/base/special/cexp/docs/img/equation_cexp_function.svg" alt="Complex exponential function">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-cexp
```

</section>

<section class="usage">

## Usage

```javascript
var cexp = require( '@stdlib/math-base-special-cexp' );
```

#### cexp( z )

Evaluates the [exponential][exponential-function] function for a double-precision complex floating-point number.

```javascript
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var v = cexp( new Complex128( 0.0, 0.0 ) );
// returns <Complex128>[ 1.0, 0.0 ]

v = cexp( new Complex128( 0.0, 1.0 ) );
// returns <Complex128>[ ~0.540, ~0.841 ]
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var cexp = require( '@stdlib/math-base-special-cexp' );

function randomComplex() {
    var re = discreteUniform( -50, 50 );
    var im = discreteUniform( -50, 50 );
    return new Complex128( re, im );
}

var z1;
var z2;
var i;
for ( i = 0; i < 100; i++ ) {
    z1 = randomComplex();
    z2 = cexp( z1 );
    console.log( 'cexp(%s) = %s', z1.toString(), z2.toString() );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/cexp.h"
```

#### stdlib_base_cexp( z )

Evaluates the [exponential][exponential-function] function for a double-precision complex floating-point number.

```c
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/real.h"
#include "stdlib/complex/float64/imag.h"

stdlib_complex128_t z = stdlib_complex128( 0.0, 0.0 );
stdlib_complex128_t out = stdlib_base_cexp( z );

double re = stdlib_complex128_real( out );
// returns 1.0

double im = stdlib_complex128_imag( out );
// returns 0.0
```

The function accepts the following arguments:

-   **z**: `[in] stdlib_complex128_t` input value.

```c
stdlib_complex128_t stdlib_base_cexp( const stdlib_complex128_t z );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/cexp.h"
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/reim.h"
#include <stdio.h>

int main( void ) {
    const stdlib_complex128_t x[] = {
        stdlib_complex128( 3.14, 1.5 ),
        stdlib_complex128( -3.14, -1.5 ),
        stdlib_complex128( 0.0, 0.0 ),
        stdlib_complex128( 0.0/0.0, 0.0/0.0 )
    };

    stdlib_complex128_t v;
    stdlib_complex128_t y;
    double re1;
    double im1;
    double re2;
    double im2;
    int i;
    for ( i = 0; i < 4; i++ ) {
        v = x[ i ];
        y = stdlib_base_cexp( v );
        stdlib_complex128_reim( v, &re1, &im1 );
        stdlib_complex128_reim( y, &re2, &im2 );
        printf( "cexp(%lf + %lfi) = %lf + %lfi\n", re1, im1, re2, im2 );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/math-base-special-cexp/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-cexp/blob/deno/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-cexp/main/LICENSE

[exponential-function]: https://en.wikipedia.org/wiki/Exponential_function

</section>

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