The complex number w is defined by \(w = \frac{22 + 4i}{(2 - i)^2}\).

1. Without using a calculator, show that \(w = 2 + 4i\). [3]
2. It is given that p is a real number such that \(\frac{1}{4}\pi \leq \text{arg}(w + p) \leq \frac{3}{4}\pi\). Find the set of possible values of p. [3]
3. The complex conjugate of w is denoted by w*. The complex numbers w and w* are represented in an Argand diagram by the points S and T respectively. Find, in the form \(|z - a| = k\), the equation of the circle passing through S, T and the origin. [3]