Question 51
Prove that for each natural number $n \neq 2$ one cannot find complex numbers $\omega_1, \omega_2, \dots, \omega_n$ on the unit circle such that
$$
|\sum \omega_j| = |\sum \omega_j^2| = n - 1.
$$
$$
|\sum \omega_j| = |\sum \omega_j^2| = n - 1.
$$