JEE Advance - Mathematics (1983 - No. 34)
Prove that the complex numbers $${{z_1}}$$, $${{z_2}}$$ and the origin form an equilateral triangle only if $$z_1^2 + z_2^2 - {z_1}\,{z_2} = 0$$.
The statement is true and a direct consequence of geometric properties and complex number representation.
The statement is false because an equilateral triangle requires equal side lengths, not a specific algebraic relation.
The statement is true only if z1 and z2 are real numbers.
The statement is true and equivalent to (z1/z2) being a primitive sixth root of unity or z1 = z2 = 0.
The statement is false as the condition only guarantees collinearity of the points.
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