Consider a set of N previously fixed angles $\phi_i$. Let $p$ be a positive integer. If $\sum^N_{i=1} e^{ip\phi_i} = 0$, what if any restriction does this place on the value of $p$? If $\phi_i = 2\pi n_i/M$, where $M$ is a positive integer and $n_i$ is a previously fixed integer in the range $[1,M]$, and $p<M$, what restrictions if any does this place on the value of $p$?
2026-04-22 02:07:38.1776823658
Controlling the Sum of a Set of Complex Numbers
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