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Let z(1),z(2) and z(3) be three non-zero...

Let `z_(1),z_(2)` and `z_(3)` be three non-zero complex numbers and `z_(1) ne z_(2)`. If `|{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0`, prove that
(i) `z_(1),z_(2),z_(3)` lie on a circle with the centre at origin.
(ii)`arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2)`.

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