6 The complex numbers \(1 + 3 \mathrm { i }\) and \(4 + 2 \mathrm { i }\) are denoted by \(u\) and \(v\) respectively.
- Find, in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real, the complex numbers \(u - v\) and \(\frac { u } { v }\).
- State the argument of \(\frac { u } { v }\).
In an Argand diagram, with origin \(O\), the points \(A , B\) and \(C\) represent the numbers \(u , v\) and \(u - v\) respectively.
- State fully the geometrical relationship between \(O C\) and \(B A\).
- Prove that angle \(A O B = \frac { 1 } { 4 } \pi\) radians.