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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
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The correct answer is:
$0$
$z_{1}, z_{2}, 0$ are vertices of an equilateral triangle, so we have $z_{1}^{2}+z_{2}^{2}+0^{2}=z_{1} z_{2}+z_{2} \cdot 0+0 \cdot z_{1}$
$$
\Rightarrow z_{1}^{2}+z_{2}^{2}=z_{1} z_{2} \Rightarrow z_{1}^{2}+z_{2}^{2}-z_{1} z_{2}=0
$$
$$
\Rightarrow z_{1}^{2}+z_{2}^{2}=z_{1} z_{2} \Rightarrow z_{1}^{2}+z_{2}^{2}-z_{1} z_{2}=0
$$
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