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Complex numbers z(1),z(2),z(3) are the v...

Complex numbers `z_(1),z_(2),z_(3)` are the vertices of A,B,C respectively of an equilteral triangle. Show that `z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).`

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