(i) To express \(u\) in the form \(x + iy\), multiply the numerator and denominator by the conjugate of the denominator:

\(u = \frac{(7 + 4i)(3 + 2i)}{(3 - 2i)(3 + 2i)}\)

\(= \frac{21 + 14i + 12i + 8i^2}{9 + 6i - 6i - 4i^2}\)

\(= \frac{21 + 26i - 8}{9 + 4}\)

\(= \frac{13 + 26i}{13}\)

\(= 1 + 2i\)

(ii) On the Argand diagram, plot the point \(U = 1 + 2i\). The locus \(|z - u| = 2\) is a circle centered at \(U\) with radius 2.

(iii) The greatest value of \(\arg z\) occurs when \(z\) is at the point on the circle furthest from the real axis. This is when the line from the origin is tangent to the circle. The angle is given as 126.9° or 2.21 radians.