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

Suppose z is a nonzero complex number [itex]z=re^{i\theta}[/itex] . Show that z has exactly n distinct complex n-th roots given by [itex]r^{(1/n)}e^{i(2\pi k+\theta)/n}[/itex] for [itex]0\leq k\leq n-1[/itex].

3. The attempt at a solution

My attempt: [itex]z^{n}=(r\cos\theta+i\sin\theta)^{n}=r^{m}(\cos \theta+i\sin\theta)^{n}=r^{m}(\cos(n \theta)+i\sin(n \theta))=r^{m}e^{i\theta n}[/itex] ...Not sure where to go from here.

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# Homework Help: Complex n-th roots

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