Complex numbers Here's the question:
z is a complex, and if $z^5 + z^4 + z^3 + z^2 + z + 1 = 0$ then $z^6=1$.
use this fact to calculate how many answers is there for:
$$z^5 + z^4 + z^3 + z^2 + z + 1 = 0$$
Thanks.

$z^6  = 1$ if and only if $z^6 - 1 = (z-1)(z^5+z^4+z^3+z^2+z+1) = 0$. So the roots of $z^5+z^4+z^3+z^2+z+1$ consist of the roots of $z^6  = 1$ excluding the root $z = 1$, which leaves $5$ roots.
