(a) Without using a calculator, solve the equation \(iw^2 = (2 - 2i)^2\).

(b) (i) Sketch an Argand diagram showing the region \(R\) consisting of points representing the complex numbers \(z\) where \(|z - 4 - 4i| \leq 2\).

(ii) For the complex numbers represented by points in the region \(R\), it is given that \(p \leq |z| \leq q\) and \(\alpha \leq \arg z \leq \beta\). Find the values of \(p, q, \alpha\) and \(\beta\), giving your answers correct to 3 significant figures.