(i) To find \(u - v\), subtract the complex numbers: \((1 + 3i) - (4 + 2i) = -3 + i\).

To find \(\frac{u}{v}\), multiply numerator and denominator by the conjugate of the denominator: \(\frac{1 + 3i}{4 + 2i} \times \frac{4 - 2i}{4 - 2i} = \frac{(1 + 3i)(4 - 2i)}{(4 + 2i)(4 - 2i)} = \frac{4 - 2i + 12i - 6i^2}{16 + 4} = \frac{10 + 10i}{20} = \frac{1}{2} + \frac{1}{2}i\).

(ii) The argument of \(\frac{u}{v}\) is \(\frac{1}{4}\pi\) radians.

(iii) OC and BA are equal in length and parallel, as they represent the same complex number \(u - v\).

(iv) To prove angle AOB = \(\frac{1}{4}\pi\), note that \(\text{arg}(u) - \text{arg}(v) = \text{arg}\left(\frac{u}{v}\right) = \frac{1}{4}\pi\).