Μιγαδικοι

Εστω z\in \mathbb{C}

Ισχυει:

3z^7+7\bar{z}^7=10

Να δειξετε οτι:

i. z^7 =\bar{z}^7=1

ii. Οι εικονες των παραπανω μιγαδικων z ειναι ομοκυκλα σημεια

iii. Αν z\neq 1, τοτε ο αριθμος w = \frac {1+z}{1-z} ειναι φανταστικος.

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