Composition of subharmonic function with $z\mapsto z^k$ for $k\in\mathbb{N}$ is subharmonic.

Question

Let $u$ be subharmonic on a neighbourhood of $0$ and let $f: \mathbb{C}\to\mathbb{C}$ be given by $f(z) = z^k$ for some $k\in\mathbb{N}$. Prove that $u\circ f$ is also subharmonic in some neighbourhood of $0$ for all $k\in\mathbb{N}$.

Any help is appreciated.