(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Complex n-th roots

**Physics Forums | Science Articles, Homework Help, Discussion**