IAL 2022 Jan Q1

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

(a) Express the complex number

in the form $r(\cos \theta + \mathrm{i} \sin \theta)$ , where $r > 0$ and $-\pi < \theta \leqslant \pi$ .

(b) Solve the equation

giving your answers in the form $r\mathrm{e}^{\mathrm{i}\theta}$ , where $r > 0$ and $-\pi < \theta \leqslant \pi$ .