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If the complex number $z_1, z_2, 0$ are vertices of an equilateral triangle, then $z_1^2+z_2^2=$
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Verified Answer
The correct answer is:
$z_1 z_2$
If $z_1, z_2$ and $z_3$ represents the vertices of an equilateral triangle, then
$z_1^2+z_2^2+z_3^2=z_1 z_2+z_2 z_3+z_3 z_1$
In this question,
$\therefore \quad z_1^2+z_2^2=z_1 z_2$
$z_1^2+z_2^2+z_3^2=z_1 z_2+z_2 z_3+z_3 z_1$
In this question,
$\therefore \quad z_1^2+z_2^2=z_1 z_2$
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