AMC 12B 2020 Problem 23

How many integers n \geq 2 are there such that whenever z_{1}, z_{2}, \ldots, z_{n} are complex numbers such that

\left|z_{1}\right|=\left|z_{2}\right|=\ldots=\left|z_{n}\right|=1 \text { and } z_{1}+z_{2}+\ldots+z_{n}=0

then the numbers z_{1}, z_{2}, \ldots, z_{n} are equally spaced on the unit circle in the complex plane?

Answer Choices
A. 1
B. 2
C. 3
D. 4
E. 5