Do not use a calculator in answering this question.
The complex number \(-2 + \mathrm{i}\) is denoted by \(z\).
Find the real numbers \(a\) and \(b\) such that \(z = az^* + b\).[2]
The complex number \(1 - 3\mathrm{i}\) is denoted by \(w\).
Without using a calculator, evaluate \(wz - \frac{w}{z}\). Give your answer in the form \(c + d\mathrm{i}\), where \(c\) and \(d\) are real numbers.[4]