Mathematics - Complex Number Question with Solution | TestHub

$z_1,z_2,0$ are vertices of an equilateral triangle, so we have $z_1^2+z_2^2+0^2=z_1{z}_2+z_2\cdot 0+0\cdot z_1$ $$\Rightarrow z_1^2+z_2^2=z_1{z}_2\Rightarrow z_1^2+z_2^2-z_1{z}_2=0$$