Let z_1 and z_2 be two complex numbers such t | vedclass

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(C) Given $\frac{z_1}{z_2} + \frac{z_2}{z_1} = 1$.Multiplying by $z_1 z_2$,we get $z_1^2 + z_2^2 = z_1 z_2$.This can be rewritten as $z_1^2 + z_2^2 -

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$z_1, z_2$ and the origin form an equilateral triangle

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(C) Given $\frac{z_1}{z_2} + \frac{z_2}{z_1} = 1$.Multiplying by $z_1 z_2$,we get $z_1^2 + z_2^2 = z_1 z_2$.This can be rewritten as $z_1^2 + z_2^2 - z_1 z_2 = 0$.Let $z_3 = 0$ be the origin.The condition for three points $z_1, z_2, z_3$ to form an equilateral triangle is $z_1^2 + z_2^2 + z_3^2 = z_1 z_2 + z_2 z_3 + z_3 z_1$.Substituting $z_3 = 0$,we get $z_1^2 + z_2^2 = z_1 z_2$,which matches our given equation.Therefore,$z_1, z_2$ and the origin form an equilateral triangle.

Let $z_1$ and $z_2$ be two complex numbers such that $\frac{z_1}{z_2} + \frac{z_2}{z_1} = 1$. Then

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