In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Express the complex number
$$- 4 - 4 \sqrt { 3 } i$$
in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\), where \(r > 0\) and \(- \pi < \theta \leqslant \pi\)
Solve the equation
$$z ^ { 3 } + 4 + 4 \sqrt { 3 } i = 0$$
giving your answers in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\), where \(r > 0\) and \(- \pi < \theta \leqslant \pi\)