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Area Method to Find Condition for Co-Linearity

If complex nu...

Question

If complex number $z_{1}, z_{2}$ and $0$ are vertices of equilateral triangle, then $z_{1}^{2} + z_{2}^{2} - z_{1} z_{2}$ is equal to

0

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z_{1} - z_{2}

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z_{1} + z_{2}

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1

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Solution

The correct option is A $0$
Given, $z_{1}, z_{2}, 0$ are vertices of an equilateral triangle.
So, we have
$z_{1}^{2} + z_{2}^{2} + 0^{2} = z_{1} z_{2} + z_{2} .0 + 0. z_{1}$
$\Rightarrow z_{1}^{2} + z_{2}^{2} = z_{1} z_{2}$
$\Rightarrow z_{1}^{2} + z_{2}^{2} - z_{1} z_{2} = 0$
Hence, option A is correct.

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