2.14.1. Problem

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 );

# $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