If the complex number $z_1, z_2, 0$ are vertices of an equilateral triangle, then $z_1^2+z_2^2=$
If the complex number $z_1, z_2, 0$ are vertices of an equilateral triangle, then $z_1^2+z_2^2=$
$2 z_1^2 z_2^2$
$z_1^2 z_2^2$
$2 z_1 z_2$
$z_1 z_2$
Solution
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,
$\therefore \quad z_1^2+z_2^2=z_1 z_2$