multiply

Multiply two complex numbers.

Usage

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

cmul( [out,] re1, im1, re2, im2 )

Multiplies two complex numbers where each complex number is comprised of a real component re and an imaginary component im.

var v = cmul( 5.0, 3.0, -2.0, 1.0 );
// returns [ -13.0, -1.0 ]

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 = cmul( out, 5.0, 3.0, -2.0, 1.0 );
// returns <Float64Array>[ -13.0, -1.0 ]

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

var re;
var im;
var z1;
var z2;
var z3;
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 );

    re = round( randu()*100.0 ) - 50.0;
    im = round( randu()*100.0 ) - 50.0;
    z2 = new Complex128( re, im );

    o = cmul( real(z1), imag(z1), real(z2), imag(z2) );
    z3 = new Complex128( o[ 0 ], o[ 1 ] );

    console.log( '(%s) * (%s) = %s', z1.toString(), z2.toString(), z3.toString() );
}