show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity
The Attempt at a Solution
if i know z = cos(2pi/n) + isin(2pi/n) is an nth root and I'm trying to prove that z is a primitive nth root. is it correct to assume that z^k is not primitive and is therefore an nth root of unity. I just need to know if z is an nth root and i know z^k is not primitive, does it have to be an nth root? just want to make sure there are no subtleties. I have the rest of the proof. I think this is easier if I use contradiction and that would require me to assume that if z^k is not primitive that it is an nth root.