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# abs2

> Compute the squared [absolute value][absolute-value] of a complex number.

<section class="intro">

The [absolute value][absolute-value] of a complex number is defined as

<!-- <equation class="equation" label="eq:absolute_value_complex" align="center" raw="|a + bi| = \sqrt{a^2 + b^2}" alt="Absolute value"> -->

<div class="equation" align="center" data-raw-text="|a + bi| = \sqrt{a^2 + b^2}" data-equation="eq:absolute_value_complex">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/special/cabs2/docs/img/equation_absolute_value_complex.svg" alt="Absolute value">
    <br>
</div>

<!-- </equation> -->

which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var cabs2 = require( '@stdlib/math/base/special/cabs2' );
```

#### cabs2( re, im )

Computes the squared [absolute value][absolute-value] of a `complex` number comprised of a **real** component `re` and an **imaginary** component `im`.

```javascript
var y = cabs2( 5.0, 3.0 );
// returns 34.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Be careful to avoid overflow and underflow.
-   Depending on the environment, this function _may_ have better performance than computing the [absolute value][absolute-value] of a `complex` number and then squaring. Hence, where appropriate, consider using `cabs2()` over [`cabs()`][@stdlib/math/base/special/cabs].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var Complex128 = require( '@stdlib/complex/float64' );
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var real = require( '@stdlib/complex/real' );
var imag = require( '@stdlib/complex/imag' );
var cabs2 = require( '@stdlib/math/base/special/cabs2' );

var re;
var im;
var z;
var i;

for ( i = 0; i < 100; i++ ) {
    re = round( randu()*100.0 ) - 50.0;
    im = round( randu()*100.0 ) - 50.0;
    z = new Complex128( re, im );
    console.log( 'cabs2(%s) = %d', z.toString(), cabs2( real(z), imag(z) ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

[absolute-value]: https://en.wikipedia.org/wiki/Absolute_value

[@stdlib/math/base/special/cabs]: https://github.com/stdlib-js/math/tree/main/base/special/cabs

</section>

<!-- /.links -->
