For a complex number zzz, if Re(z2)=(Im(z))2\text{Re}(z^2) = (\text{Im}(z))^2Re(z2)=(Im(z))2, what is the locus of zzz?
A circle centered at origin
The line y=xy = xy=x
The lines y=±xy = \pm xy=±x
The hyperbola x2−y2=y2x^2 - y^2 = y^2x2−y2=y2