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Question Number 20619 by Tinkutara last updated on 29/Aug/17

$$Solvetheequation{z}^{n-1}=\overline{z}(n\in N)$$

Answered by ajfour last updated on 29/Aug/17

$$\mid z\mid =1$$$$z^n=\mid z{\mid }^2=1$$$$z^n=1=\cos \left(2k\pi \right)+i\sin \left(2k\pi \right)$$$$\Rightarrow z=\cos \left(\frac{2k\pi }{n}\right)+i\sin \left(\frac{2k\pi }{n}\right)$$$$wherek\in \mathbb{Z}.$$

Commented by Tinkutara last updated on 29/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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