On Thu, May 9, 2013 at 2:25 AM, Kerry Mitchell <lkmitch@gmail.com> 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?
Write your complex number z as r e^(i * t), where r and t are real. (I use t instead of the standard theta for ease of expressing in ASCII) Then the nth roots of z are r^(1/n) e^(i (2pi k + t)/n), for k = 0, 1, 2, ... n - 1. Geometrically, the n roots are evenly spaced on a circle centered at the origin. Andy
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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