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# exp

> 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="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' );
var real = require( '@stdlib/complex/real' );
var imag = require( '@stdlib/complex/imag' );

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

var re = real( v );
// returns 1.0

var im = imag( v );
// returns 0.0

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

re = real( v );
// returns ~0.540

im = imag( v );
// returns ~0.841
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var Complex128 = require( '@stdlib/complex/float64' );
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.h"
#include "stdlib/complex/real.h"
#include "stdlib/complex/imag.h"

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

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

double im = stdlib_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.h"
#include "stdlib/complex/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_reim( v, &re1, &im1 );
        stdlib_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>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

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

</section>

<!-- /.links -->
