Question

Indicate the point of the complex plane $z$ which satisfy the following equation.
$Re{z}^2=0$

Answer 1

Let $z=x+iy⟹z^2={(x+iy)}^2⟹=x^2-y^2+2ixyRe\left(z^2\right)=0\therefore x^2-y^2=0⟹(x+y)(x-y)=0$