I will state the problem here:
Let $\omega$ be a complex number such that $\omega^5 = 1$ and $\omega \neq 1$. Compute $\frac{\omega}{1 + \omega^2} + \frac{\omega^2}{1 + \omega^4} + \frac{\omega^3}{1 + \omega} + \frac{\omega^4}{1 + \omega^3}.$
W is obviously a complex number. I've tried arranging and rearranging the terms in a way to further simplify the expression, but I'm having trouble getting anywhere with it. Anyone have ideas on how to proceed and solve the problem?