The N^th root of a given number is that number raised to the reciprocal of N. Thus:

Update: Heh. Looks like I beat the rush. Is this where I delete everything and replace it with "first post!"? :)

Update: As pointed out below, c=r^(1/n)*e^(2*pi*i*j/n) (for j=0,1,...,n-1) will do the trick, but I was thinking someone should have written an easy access to the roots, as in:

@roots=complex_roots($real, $n)
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You can use trig and brute force a method -- I'm a little busy to give it a go, but the complex roots lie on a circle in the complex plane of the same radius as the real root. With a cube root, that means you need to find the coords of the points at 120 and 240 degrees (1/3 and 2/3 around the circle) on that circle -- hopefully that's clear. For the nth root you need to look at the (i * 360/n) degree points with i = 0..(n-1). i=0 corresponds to the real root.

Update:

#!/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;
}
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print 8 ** (1/3);   # prints 2
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small math lesson for AM: just incase you didn't realize, taking the nth root of anything is the same as raising that expression/number/etc..etc..etc... to the 1/n power where n is the root you are trying to find.

to find the 5th root of x, you simply do x**(1/5), 218th root x**(1/218), you get the picture. FYI: very much respect for the question, but just not a perl way of doing it.. just a math way. You can write your own sub to do it if you really wanna make it readable for newbies or non-coders.

#!/perl

use strict;

#Take the 3rd root of 8;
my $root = nthRoot(8,3);

print $root;

#Just pull the parameters off the 
#@_ array as they are needed
#in the return statement
sub nthRoot
{return (shift)**(1/shift);}
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