(a)[6]
It is given that $(1 + 3i)w = 2 + 4i$. Show all the working needed to prove that the exact value of $|w^2|$ equals $2$ and determine $\arg(w^2)$ correct to $3$ significant figures.
(b)[4]
On one Argand diagram, sketch the loci $|z| = 5$ and $|z - 5| = |z|$. Hence determine the complex numbers at the points shared by both loci, with each answer written in the form $re^{i\theta}$.