(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that [itex]z=e^{\frac{2k\pi i}{n}},n\in\mathbb{N},k\in\mathbb{Z}, 0\leq k\leq n-1 [/itex] is an n-th root of unity.

3. The attempt at a solution

So I know I have to come to the conclusion that [itex]z^{n}=1[/itex]. I'm thinking of using the property [itex]e^{i\theta}=cos\theta+isin\theta[/itex], but when I try to break it up like that I get something strange like [itex]e^{\frac{2k\pi i}{n}}=cos(\frac{2k\pi}{n})+i( \frac{2k\pi}{n})[/itex] and I have to get it into a form like [itex]cos^{2}(\theta)+sin^{2}(\theta) [/itex]. Any ideas on how to do that/am I on the right track?

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# N-th root of unity

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