So let me take a whack at this, and also solve a few bugs:

use Math::Complex;
use CGI qw(param);

for my $i (1..$varno) {
  for my $j (1..$varno) {
    next unless my $val = param("val-$i-$j");
    if (my($re, $im) = $val =~ /(.*)([-+].*)[ij]/) {
      $matrix[$i][$j] = cplx($re, $im);
    } else {
      $matrix[$i][$j] = cplx($val, 0);
    }
  }
}
[download]

I still don't entirely like the complex parsing. But at least now I can say 5-3j, unlike your code where you had to say 5+-3j. Oddly enough, I don't know why Math::Complex doesn't have an input parser. It should!

-- Randal L. Schwartz, Perl hacker