(a) The complex number u is defined by \(u = \frac{5}{a + 2i}\), where the constant a is real.

1. Express u in the form x + iy, where x and y are real.
2. Find the value of a for which \(\arg(u^*) = \frac{3}{4}\pi\), where u* denotes the complex conjugate of u.

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