$z_1,...z_n$ are the $n$ solutions of $z^n =a$ and $a$ is real number, show that $z_1+...+z_n$ is a real number I was actually trying this simple question, might be just me being really rusty not doing maths for a very long time. I tried adding all the $\theta$ up on all zs but it doesn't seem to work.
Anyway as the title states,
$z_1,...z_n$ are the $n$ solutions of  $z^n =a$ and $a$ is real number, show that $z_1+...+z_n$ is a real number.

Use thae fact that $$z^n -a =z^n -(z_1 +...+z_n ) z^{n-1} +...+ z_1 \cdot z_2 \cdot ...\cdot z_n $$
