Roots of unity

  • Thread starter Driessen12
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  • #1
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Homework Statement



show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity

Homework Equations





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.
 

Answers and Replies

  • #2
Landau
Science Advisor
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I think it will be quite helpful (to you) to state the precise definitions of (n-th) root and primitive (n-th) root of unity. Also [URL [Broken] Moivre[/url] can be useful here.
 
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