Prove that the complex numbers `z_(1),z_(2)` and the origin form an equilateral triangle only if `z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0`.

Prove that the complex numbers `z_(1),z_(2)` and the origin form an eq

1.	Prove that the complex numbers `z_(1),z_(2)` and the origin form an equilateral triangle only if `z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0`.
Answer» We know that if `z_(1),z_(2)` and `z_(3)` from an equilateral trinagle , then `z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = z_(1)z_(2) + z_(2)z_(3) + z_(3)z_(1)` Putting `z_(3) = 0`, we get `z_(1)^(2) + z_(2)^(2) - z_(1)z_(2) =0`

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Prove that the complex numbers `z_(1),z_(2)` and the origin form an equilateral triangle only if `z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0`.

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