#!/usr/bin/perl -w
use strict;

my $twoPi = 4 * atan2(1, 0);

for (2..5) {
  my @roots = nthRoots(8, $_);
  print "$_ th roots of 8: $/";
  foreach my $root (@roots) {
    print "$root->{Real} $root->{Imag}$/";
  }
};

sub nthRoots {
  my $x = shift;
  my $n = shift;
  # Should check for integer powers
  my @roots;
  $roots[0] = {
                Real => $x ** (1/$n),
                Imag => 0
               };
  for (1..($n-1)) {
    push @roots, {
                  Real => $roots[0]->{Real} * cos( $_ * $twoPi/$n ),
                  Imag => $roots[0]->{Real} * sin( $_ * $twoPi/$n )
                  };
  };
	
  return @roots;
}