(a)[5]
The complex number $u$ is $u = 8 - 15i$. With full working shown, determine the two square roots of $u$. Express your answers in the form $a + ib$, where $a$ and $b$ are exact real numbers.
(b)[4]
On an Argand diagram, shade the set of points representing complex numbers that satisfy both inequalities $|z - 2 - i| \le 2$ and $0 \le \arg(z - i) \le \frac{1}{4}\pi$.