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prove that for all complex numbers z,  the conjugate(z)^n= conjugate(z^n)

 Jun 20, 2021
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In polar coordinates:  \(z=re^{i\theta} \text{ and } \bar{z} = re^{-i\theta}\)   so \((\bar{z})^n=(re^{-i\theta})^n=r^ne^{-in\theta}\) and \(\bar{z^n}=\bar{(r^ne^{in\theta})}=r^ne^{-in\theta}\)

 Jun 20, 2021

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