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