2. The complex numbers \(z _ { 1 }\) and \(z _ { 2 }\) are given by
$$z _ { 1 } = 3 + 5 i \text { and } z _ { 2 } = - 2 + 6 i$$
- Show \(z _ { 1 }\) and \(z _ { 2 }\) on a single Argand diagram.
- Without using your calculator and showing all stages of your working,
- determine the value of \(\left| z _ { 1 } \right|\)
- express \(\frac { z _ { 1 } } { z _ { 2 } }\) in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are fully simplified fractions.
- Hence determine the value of \(\arg \frac { Z _ { 1 } } { Z _ { 2 } }\)
Give your answer in radians to 2 decimal places.