a) Use the fact that zz = |z|² for all z EC to prove that \left|z_{1} z_{2}\right|=\left|z_{1}\right|\left|z_{2}\right| \quad \forall z_{1}, z_{2} \in \mathbb{C} . Show that the equation (z+\bar{z})^{2}=2 i(z-\bar{z}), \quad z \in \mathbb{C} represents a parabola in the complex plane.