4.
$$z = - 8 + ( 8 \sqrt { } 3 ) \mathrm { i }$$
- Find the modulus of \(z\) and the argument of \(z\).
Using de Moivre's theorem,
- find \(z ^ { 3 }\),
- find the values of \(w\) such that \(w ^ { 4 } = z\), giving your answers in the form \(a + \mathrm { i } b\), where \(a , b \in \mathbb { R }\).