(a) If

$$x+i y=\sum_{a=0}^{200} i^{a}+\prod_{b=1}^{50} i^{b}$$

where $x, y \in \mathbb{R}$, what is the value of $x y$ ?

(b) Evaluate

$$\frac{(1+i)^{2019}}{(1-i)^{2017}}$$

(c) Find a complex number $z$ such that

$$i^{i^{z}}=2$$

(d) Interpret geometrically the curve defined by the set of points satisfying

$$\log z=i \log \bar{z}$$

in the complex $z$-plane.