(a) The complex number \(\frac{3 - 5i}{1 + 4i}\) is denoted by \(u\). Showing your working, express \(u\) in the form \(x + iy\), where \(x\) and \(y\) are real.

(b) (i) On a sketch of an Argand diagram, shade the region whose points represent complex numbers satisfying the inequalities \(|z - 2 - i| \leq 1\) and \(|z - i| \leq |z - 2|\).

(ii) Calculate the maximum value of \(\arg z\) for points lying in the shaded region.