Question

The number of solutions of the equation $z^2+\overline{z}=0$ is: (where z is a complex number)

Answer 1

$\begin{array}{c}{Z}^2+\overline{Z}=0\\ Z=x+iy\to \left(let\right)\\ Z=-1+0i\left\{takey=0\right\}\\ Z=\frac{1}{2}+\frac{\sqrt{2}}{2}i\left\{takex=\frac{1}{2}\right\}\\ Hence,\\ Z=\frac{1}{2}-\frac{\sqrt{3}}{2}i\end{array}$