4. A complex number is defined by \(z = - 3 + 4 \mathrm { i }\).
- Express \(z\) in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\), where \(- \pi \leqslant \theta \leqslant \pi\).
- Express \(\bar { z }\), the complex conjugate of \(z\), in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\).
Another complex number is defined as \(w = \sqrt { 5 } ( \cos 2 \cdot 68 + \mathrm { i } \sin 2 \cdot 68 )\).
- Express \(z w\) in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\).