(i) To find u - 2w, calculate:

\(u - 2w = (-1 + 7i) - 2(3 + 4i) = -1 + 7i - 6 - 8i = -7 - i\)

To find \(\frac{u}{w}\), multiply numerator and denominator by the conjugate of the denominator:

\(\frac{u}{w} = \frac{-1 + 7i}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{(-1 + 7i)(3 - 4i)}{(3 + 4i)(3 - 4i)}\)

Calculate the denominator:

\((3 + 4i)(3 - 4i) = 9 + 16 = 25\)

Calculate the numerator:

\((-1 + 7i)(3 - 4i) = -3 + 4i + 21i - 28i^2 = -3 + 25i + 28 = 25 + 25i\)

Thus, \(\frac{u}{w} = \frac{25 + 25i}{25} = 1 + i\)

(ii) The argument of \(\frac{u}{w} = 1 + i\) is \(\arctan(1) = \frac{\pi}{4}\).

\((iii) Since u - 2w = -7 - i, OB and CA are parallel and CA = 2OB.\)