(A) Let $f$ be an entire function such that $|f(z)| \leq |z|$. Show that $f$ is a polynomial of degree $\leq 1$.\\
(B) Let $\Gamma$ be a closed differentiable contour oriented counterclockwise and let
$$\int_{\Gamma} \bar{z} \, \mathrm{d}z = A$$
What is the integral
$$\int_{\Gamma} (x + y) \, \mathrm{d}z$$
(where $x$ and $y$, respectively, are the real and imaginary parts of $z$) in terms of $A$?