Suppose that $\phi$ is an endomorphism of a finite-dimensional complex vector space.

(i) Show that if $\lambda$ is an eigenvalue of $\phi$, then $\lambda^{2}$ is an eigenvalue of $\phi^{2}$.

(ii) Show conversely that if $\mu$ is an eigenvalue of $\phi^{2}$, then there is an eigenvalue $\lambda$ of $\phi$ with $\lambda^{2}=\mu$.