2.
$$z = - 2 + ( 2 \sqrt { 3 } ) \mathrm { i }$$
- Find the modulus and the argument of \(z\).
Using de Moivre's theorem,
- find \(z ^ { 6 }\), simplifying your answer,
- find the values of \(w\) such that \(w ^ { 4 } = z ^ { 3 }\), giving your answers in the form \(a + \mathrm { i } b\) where \(a , b \in \mathbb { R }\).