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2019 AMC 12B Question 17

AMC12 · 2019 AMC 12B

Question 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?
  1. $0$
  2. $1$
  3. $2$
  4. $4$
  5. infinitely many