Max Distance Between Cubic Roots

1550AdeptPolynomialsComplex Numbers

AMC 12A · 2020 · Problem 15

In the complex plane, let $A$ be the set of solutions to $z^3 - 8 = 0$ and let $B$ be the set of solutions to $z^3 - 8z^2 - 8z + 64 = 0$. What is the greatest distance between a point of $A$ and a point of $B?$

Answer choices

2\sqrt{3}

2\sqrt{21}

9 + \sqrt{3}

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