I have this question that I have no idea how to approach!
Let $w_{1},w_{2},...,w_{n}$ be complex numbers such that there exists a constant $C$ such that $|w_{1}^k+ w_{2}^k + ... + w_ {n}^k| \leq C$ for all whole numbers $k \geq 0$. Show that $|w_{j}| \leq 1$ for all $j$
Thankful for any help!