(a)[3]
Write $z^2$ in the form $re^{i\theta}$, with $r > 0$ and $-\pi < \theta \leq \pi$.
(b)[3]
The complex number $\omega$ satisfies $z^2\,\omega$ being real and $\left|\frac{z^2}{\omega}\right| = 12$. Determine the two possible values of $\omega$, with answers written in the form $Re^{i\alpha}$, where $R > 0$ and $-\pi < \alpha \leq \pi$.