(a)[5]
Showing your working, determine the two square roots of the complex number $1 - 2\sqrt{6}i$. Present your answers in the form $x + iy$, with $x$ and $y$ exact.
(b)[5]
On a sketch of an Argand diagram, shade the set of points for the complex numbers $z$ that satisfy $|z - 3i| \leq 2$. Determine the largest value of $\arg z$ for points in this set.