jasperE3 22.04.2021 16:08 Let $z\ne0$ be a complex number such that $z^8=\overline z$. What are the possible values of $z^{2001}$?
DottedCaculator 22.04.2021 16:14 |z^8|=|z| |z|^8=|z| |z|=0, 1 |z|=1 z^8=1/z z^9=1 z^2001=z^3 z^3=1,1/2+-sqrt3/2 i
Alan-Z 01.05.2021 15:31 $|z^8|=|z|$ $|z|^8=|z|$ So $|z|=0,1$ $|z|=1$ $z^8=\frac{1}{z}$ $z^9=1$ $z^{2001}=z^3$ $z^3=1,\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$