cis

Compute the cis function of a complex number.

The cis function is defined as

c i s left-parenthesis z right-parenthesis equals e Superscript i z Baseline equals cosine left-parenthesis z right-parenthesis plus i sine left-parenthesis z right-parenthesis

Usage

var cis = require( '@stdlib/math/base/complex/cis' );

cis( [out,] re, im )

Evaluates the cis function with a complex argument comprised of a real component re and an imaginary component im.

var v = cis( 0.0, 0.0 );
// returns [ 1.0, 0.0 ]

v = cis( 1.0, 0.0 );
// returns [ ~0.540, ~0.841 ]

By default, the function returns real and imaginary components as a two-element array. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

var Float64Array = require( '@stdlib/array/float64' );

var out = new Float64Array( 2 );

var v = cis( out, 1.0, 0.0 );
// returns <Float64Array>[ ~0.540, ~0.841 ]

var bool = ( v === out );
// returns true

Examples

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 cis = require( '@stdlib/math/base/complex/cis' );

var re;
var im;
var z1;
var z2;
var o;
var i;

for ( i = 0; i < 100; i++ ) {
    re = round( randu()*100.0 ) - 50.0;
    im = round( randu()*100.0 ) - 50.0;
    z1 = new Complex128( re, im );

    o = cis( [ 0.0, 0.0 ], real(z1), imag(z1) );
    z2 = new Complex128( o[ 0 ], o[ 1 ] );

    console.log( 'cis(%s) = %s', z1.toString(), z2.toString() );
}