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If the points `z_(1),z_(2),z_(3)` are the vertices of an equilateral triangle in the Argand plane, then which one of the following is not correct?

A

`(1)/( z_(1) - z_(2)) + (1)/( z_(2) - z_(3)) + (1)/( z_(3) - z_(1)) = 0 `

B

` z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = z_(1) z_(2) + z_(2) z_(3) + z_(3) z_(1)`

C

`(z_(1) - z_(2))^(2) + (z_(2) - z_(3))^(2) + (z_(3) - z_(1)) ^(2) = 0 `

D

`z_(1)^(3) + z_(2)^(3) + z_(3)^(3) + 3 z_(1)z_(2)z_(3) = 0 `

Text Solution

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The correct Answer is:
A, B, C
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