- In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
$$z _ { 1 } = 3 + 2 i \quad z _ { 2 } = 2 + 3 i \quad z _ { 3 } = a + b i \quad a , b \in \mathbb { R }$$
- Determine the exact value of \(\left| z _ { 1 } + z _ { 2 } \right|\)
Given that \(w = \frac { z _ { 2 } z _ { 3 } } { z _ { 1 } }\)
- determine \(w\) in terms of \(a\) and \(b\), giving your answer in the form \(x + \mathrm { i } y\), where \(x , y \in \mathbb { R }\)
Given also that \(w = \frac { 4 } { 13 } + \frac { 58 } { 13 } \mathrm { i }\)
- determine the value of \(a\) and the value of \(b\)
- determine arg \(w\), giving your answer in radians to 4 significant figures.