2020 AMC 12B Problem 23

For $n = 2,$ $z_1 + z_2 = 0$ forces $z_2 = -z_1,$ which is equally spaced. For $n = 3,$ three unit vectors summing to zero must form an equilateral triangle, so they are equally spaced. For every even $n\ge4,$ choose $\frac{n}{2}$ antipodal pairs at generic angles that do not form a regular $n$-gon. For every odd $n\ge5,$ choose the vertices of an equilateral triangle together with $\frac{n-3}{2}$ generic antipodal pairs. Each construction has sum $0$ but is not equally spaced. Hence only $n = 2$ and $n = 3$ work, giving $2$ values. Thus, the correct answer is B.