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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