froom my textbook it writes:

de moivre's thm

$\displaystyle (cosx + i sin x )^{\frac p q } = cos (\frac p q x + \frac {2k\pi} q ) + i sin (\frac p q x + \frac {2k\pi} q )$

for$\displaystyle k = 0, 1, 2, ... , q-1$

i don't understand why k cannot be greater than q-1. thanks