Question 23
How many integers $n \ge 2$ are there such that whenever $z_1,$ $z_2,$ $\ldots,$ $z_n$ are complex numbers such that $$
|z_1| = |z_2| = \cdots = |z_n| = 1
$$ and $$
z_1 + z_2 + \cdots + z_n = 0,
$$ then the numbers $z_1,$ $z_2,$ $\ldots,$ $z_n$ are equally spaced on the unit circle in the complex plane?
|z_1| = |z_2| = \cdots = |z_n| = 1
$$ and $$
z_1 + z_2 + \cdots + z_n = 0,
$$ then the numbers $z_1,$ $z_2,$ $\ldots,$ $z_n$ are equally spaced on the unit circle in the complex plane?