Recipe 2.14 Using Complex Numbers

2.14.1 Problem

Your application must manipulate complex numbers, as are often needed in engineering, science, and mathematics.

2.14.2 Solution

Either keep track of the real and imaginary components yourself:

# $c = $a * $b manually
$c_real = ( $a_real * $b_real ) - ( $a_imaginary * $b_imaginary );
$c_imaginary = ( $a_real * $b_imaginary ) + ( $b_real * $a_imaginary );

or use the Math::Complex module (part of the standard Perl distribution):

# $c = $a * $b using Math::Complex
use Math::Complex;
$c = $a * $b;

2.14.3 Discussion

Here's how you'd manually multiply 3+5i and 2-2i:

$a_real = 3; $a_imaginary = 5;              # 3 + 5i;
$b_real = 2; $b_imaginary = -2;             # 2 - 2i;
$c_real = ( $a_real * $b_real ) - ( $a_imaginary * $b_imaginary );
$c_imaginary = ( $a_real * $b_imaginary ) + ( $b_real * $a_imaginary );
print "c = ${c_real}+${c_imaginary}i\n";

c = 16+4i

and with Math::Complex:

use Math::Complex;
$a = Math::Complex->new(3,5);               # or Math::Complex->new(3,5);
$b = Math::Complex->new(2,-2);
$c = $a * $b;
print "c = $c\n";

c = 16+4i

You may create complex numbers via the cplx constructor or via the exported constant i:

use Math::Complex;
$c = cplx(3,5) * cplx(2,-2);                # easier on the eye
$d = 3 + 4*i;                               # 3 + 4i
printf "sqrt($d) = %s\n", sqrt($d);

sqrt(3+4i) = 2+i

The Math::Trig module uses the Math::Complex module internally because some functions can break out from the real axis into the complex planefor example, the inverse sine of 2.