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Let the complex numbers `z_(1),z_(2)` and `z_(3)` be the vertices of an equailateral triangle. If `z_(0)` is the circumcentre of the triangle , then prove that ` z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3z_(0)^(2)`.

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The correct Answer is:
`rArr 3 z_(0)^(2) = z_(1)^(2) + z_(2)^(2) + z_(3)^(2)`
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