Given $u$, a subharmonic function near $0$, proof that $u(z^k)$ is also subharmonic.

Question

I am following Thomas Ransford's book Potential Theory on the Complex Plane. I am stuck with exercise 2.4.2.i, page 39:

Show that if $u(z)$ is subharmonic on a neighborhood of $0$, then so is $u(z^k)$ for each $k\geq 1$.

I solved 2.4.2.ii and 2.4.2.iii, but the above proposition is still "unsolved". Any suggestion will be appreciated.