Let , ² be the complex cube roots of unity. Let z₁, Z₂, Z3 be complex numbers such that Z₁ + Z₂ +Z₁ = A z₁ + @z₂ +w²z₂ = B z₁ + @²z₂ + @z₂ = C. Evaluate z₁,z₂ and z, in terms of A, B, and C.

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A: Introduction :

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