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Found problems: 1

2019 AMC 12/AHSME, 17
How many nonzero complex numbers $z$ have the property that $0, z,$ and $z^3,$ when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle? $\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }4\qquad\textbf{(E) }\text{infinitely many}$
amc 12b 17 complex number algebra complex numbers geometry law of cosines modular arithmetic