We are given a polynomial $P \in \mathbb{C}[X]$ of degree $d$. Show that, for all $z \in \mathbb{C}$ and all $r \in \mathbb{R}$, we have: $$P(z) = \frac{1}{2\pi} \int_0^{2\pi} P\left(z + re^{i\theta}\right) d\theta$$
We are given a polynomial $P \in \mathbb{C}[X]$ of degree $d$. Show that, for all $z \in \mathbb{C}$ and all $r \in \mathbb{R}$, we have:
$$P(z) = \frac{1}{2\pi} \int_0^{2\pi} P\left(z + re^{i\theta}\right) d\theta$$