The complex number 2 + 2i is denoted by u.

(i) Find the modulus and argument of u.

(ii) Sketch an Argand diagram showing the points representing the complex numbers 1, i and u. Shade the region whose points represent the complex numbers z which satisfy both the inequalities \(|z - 1| \leq |z - i|\) and \(|z - u| \leq 1\).

(iii) Using your diagram, calculate the value of \(|z|\) for the point in this region for which \(\arg z\) is least.