# How Square are the Cube Roots of Unity?

Algebra Level 4

$\Large{z^3=1}$ Let $$z_1,z_2,z_3$$ be the cube roots of unity satisfying the equation above. If $$a\in\{1,2,3\}$$ and $$b\in\{1,2,3\}$$,when is it true that $$z^{2}_a= z_b$$ ?

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