Solve the equation $\;z^{2} = \overline{z}\;$ where $\;z=x+iy$

Question

$(a)\;\large\frac{7}{2} \pm \large\frac{\sqrt{3}}{2}\qquad(b)\;-\large\frac{1}{2} \pm \large\frac{\sqrt{3}}{2}\qquad(c)\;-\large\frac{3}{2} \pm \large\frac{\sqrt{5}}{2}\qquad(d)\;-\large\frac{5}{2} \pm \large\frac{\sqrt{3}}{2}$