# abs2
> Compute the squared [absolute value][absolute-value] of a complex number.
The [absolute value][absolute-value] of a complex number is defined as
which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.
## 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
```
## 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].
## Examples
```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) ) );
}
```
[absolute-value]: https://en.wikipedia.org/wiki/Absolute_value
[@stdlib/math/base/special/cabs]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cabs
