Question

If $n$ is the number of roots (real or imaginary ) of the following complex equation $z^{100}=\overline{z}$ then $\left[\frac{n}{17}\right]$ is

Answer 1

$z^{100}=\overline{z}\Rightarrow z^{100}=|\overline{z}|\Rightarrow |z|=0,1$

Also, $z^{101}=z.\overline{z}=|z{|}^2=1orz=0$

Hence $n=102$

$\therefore \left[\frac{102}{17}\right]=6$