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Equilateral Triangle from z and z³

1675AdeptComplex NumbersGeometry

AMC 12B · 2019 · Problem 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?

Answer choices

A
0
B
1
C
2
D
4
E
\text{infinitely many}
0 students attempted0% solvedRating 1675

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