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If z(1),z(2)andz(3) are the vertices of...

If `z_(1),z_(2)andz_(3)` are the vertices of an equilasteral triangle with `z_(0)` as its circumcentre , then changing origin to `z^(0)` ,show that `z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0,` where`z_(1),z_(2),z_(3),` are new complex numbers of the vertices.

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