[math-fun] z^n = 1 for Gaussian integer n

Hi all, I am playing with a problem that has boiled down to this: for positive integer n, there are n complex roots of 1 (or any complex number). What happens when n is a Gaussian integer? How many roots are there and what are they like? I've done some preliminary work on this; can someone point me to a reference so I can see if I'm on the right track? Thanks, Kerry