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2.14.1. Problem

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 );

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 documentation for the standard Math::Complex module (also in
Chapter 32 of Programming Perl)

2.13. Multiplying Matrices		2.15. Converting Binary, Octal, and Hexadecimal Numbers