2.
$$z = 6 - 6 \sqrt { 3 } i$$
- Determine the modulus of \(z\)
- Show that the argument of \(z\) is \(- \frac { \pi } { 3 }\)
Using de Moivre's theorem, and making your method clear,
- determine, in simplest form, \(z ^ { 4 }\)
- Determine the values of \(w\) such that \(w ^ { 2 } = z\), giving your answers in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real numbers.