(a)[5]
The complex number $u$ is defined by $u = -3 - (2\sqrt{10})i$. With all working shown and no calculator used, determine the square roots of $u$. Present your answers in the form $a + ib$, where $a$ and $b$ are exact real numbers.
(b)[5]
On a sketch of an Argand diagram, shade the set of points corresponding to complex numbers $z$ that satisfy $|z - 3 - i| \leq 3$, $\arg z \geq \frac{\pi}{4}$ and $\operatorname{Im} z \geq 2$, where $\operatorname{Im} z$ is the imaginary part of the complex number $z$.