Problem

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

The complex number $z$ is defined by

$z = -3 + 4\mathrm{i}$

(a) Determine $|z|^2 - 3$

(b) Express $\dfrac{50}{z^*}$ in the form $kz$, where $k$ is a positive integer.

(c) Hence find the value of $\arg\left(\dfrac{50}{z^*}\right)$

Give your answer in radians to 3 significant figures.