(a) Let

$$z=2+2 i$$

(i) Compute $z^{4}$.

(ii) Find all complex numbers $w$ such that $w^{4}=z$.

(b) Find all the solutions of the equation

$$e^{2 z^{2}}-1=0$$

(c) Let $z=x+i y, \bar{z}=x-i y, x, y \in \mathbb{R}$. Show that the equation of any line, and of any circle, may be written respectively as

$$B z+\bar{B} \bar{z}+C=0 \quad \text { and } \quad z \bar{z}+\bar{B} z+B \bar{z}+C=0$$

for some complex $B$ and real $C$.