(a)[2]
For the complex number $u = \frac{(\cos \frac{\pi}{7} + i \sin \frac{\pi}{7})^4}{\cos \frac{\pi}{7} - i \sin \frac{\pi}{7}}$, find the exact value of $\arg u$.
(b)[2]
On an Argand diagram, the complex numbers $u$ and $u^*$ are shown. Describe the one geometric transformation that sends $u$ to $u^*$ and state the exact value of $\arg u^*$.