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z3=1\Large{z^3=1}z3=1 Let z1,z2,z3z_1,z_2,z_3z1,z2,z3 be the cube roots of unity satisfying the equation above. If a∈{1,2,3}a\in\{1,2,3\}a∈{1,2,3} and b∈{1,2,3}b\in\{1,2,3\}b∈{1,2,3},when is it true that za2=zbz^{2}_a= z_bza2=zb ?
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