Make it easier on yourself and use stuff that's already available...

#!/usr/bin/perl -w

use strict;
use Math::Complex; # http://perldoc.perl.org/Math/Complex.html

my $a = toComplex("1-4i");
my $b = toComplex("2+7j");
my $c = toComplex("3 _ 2");
my $d = toComplex("5 _ 0.707");

$\ = "\n";
print $a + $b;
print $c * $d;

sub toComplex
{
    my $str = shift;

    $str =~ tr/j/i/; # convert j's to i's
    $str =~ s/(.*)_(.*)/[$1,$2]/; # convert "_" into something that 
                                  # Math::Complex will like

    return Math::Complex->make($str);
}
[download]