How Square are the Cube Roots of Unity?

Algebra Level 4

z3=1\Large{z^3=1} Let z1,z2,z3z_1,z_2,z_3 be the cube roots of unity satisfying the equation above. If a{1,2,3}a\in\{1,2,3\} and b{1,2,3}b\in\{1,2,3\},when is it true that za2=zbz^{2}_a= z_b ?

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