- In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
$$z _ { 1 } = - 4 + 4 i$$
- Express \(\mathrm { z } _ { 1 }\) in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\), where \(r \in \mathbb { R } , r > 0\) and \(0 \leqslant \theta < 2 \pi\)
$$z _ { 2 } = 3 \left( \cos \frac { 17 \pi } { 12 } + i \sin \frac { 17 \pi } { 12 } \right)$$
- Determine in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are exact real numbers,
- \(\frac { Z _ { 1 } } { Z _ { 2 } }\)
- \(\left( z _ { 2 } \right) ^ { 4 }\)
- Show on a single Argand diagram
- the complex numbers \(z _ { 1 } , z _ { 2 }\) and \(\frac { z _ { 1 } } { z _ { 2 } }\)
- the region defined by \(\left\{ z \in \mathbb { C } : \left| z - z _ { 1 } \right| < \left| z - z _ { 2 } \right| \right\}\)