2. Show that if $f$ is analytic on $D$, then $g(z) = \overline{f(\overline{z})}$ is analytic on the reflected domain $D^* = \{\overline{z} | z \in D\}$, with derivative $g'(z) = \overline{f'(\overline{z})}$.
3. Let $h: [0, 1] \to \mathbb{C}$ be continuous, and define $H: \mathbb{C} \setminus [0, 1] \to \mathbb{C}$ by
$$H(z) = \int_0^1 \frac{h(t)}{t - z} dt.$$
