7.
$$z _ { 1 } = 2 + 3 \mathrm { i } , \quad z _ { 2 } = 3 + 2 \mathrm { i } , \quad z _ { 3 } = a + b \mathrm { i } , \quad a , b \in \mathbb { R }$$
- Find the exact value of \(\left| z _ { 1 } + z _ { 2 } \right|\).
Given that \(w = \frac { z _ { 1 } z _ { 3 } } { z _ { 2 } }\),
- find \(w\) in terms of \(a\) and \(b\), giving your answer in the form \(x + \mathrm { i } y , \quad x , y \in \mathbb { R }\)
Given also that \(w = \frac { 17 } { 13 } - \frac { 7 } { 13 } \mathrm { i }\),
- find the value of \(a\) and the value of \(b\),
- find \(\arg w\), giving your answer in radians to 3 decimal places.