The complex numbers \(-2 + i\) and \(3 + i\) are denoted by \(u\) and \(v\) respectively.

(i) Find, in the form \(x + iy\), the complex numbers

(a) \(u + v\),

(b) \(\frac{u}{v}\), showing all your working.

(ii) State the argument of \(\frac{u}{v}\).

In an Argand diagram with origin \(O\), the points \(A, B\) and \(C\) represent the complex numbers \(u, v\) and \(u + v\) respectively.

(iii) Prove that angle \(AOB = \frac{3}{4}\pi\).

(iv) State fully the geometrical relationship between the line segments \(OA\) and \(BC\).