$\textbf{Question:}$ Describe the locus of points z satisfying the given equation: $Re(z^2) = 4$.
$\textbf{Answer:}$
Let $z=x+iy$,
$z^2 = (x+iy) (x+iy) = x^2-y^2+(2xy)i$.
Thus, $Re(z^2) = x^2-y^2=4$.
Therefore, the locus of points z is a hyperbola with equation $x^2-y^2=4$.
