The map of Gaussian integers in the complex plane has symmetries around the x & y axes and the x=+-y lines. If you take the square root, you get 2 copies, but unrolled (about the origin). If you take the cube root, you get 3 copies, with hexagon & other symmetries. Yes, each point in the original map maps to n points in the root(n,x) map. Etc. At 11:25 PM 5/8/2013, Kerry Mitchell wrote:

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