5 Throughout this question the use of a calculator is not permitted.
The complex numbers \(w\) and \(z\) satisfy the relation
$$w = \frac { z + \mathrm { i } } { \mathrm { i } z + 2 }$$
- Given that \(z = 1 + \mathrm { i }\), find \(w\), giving your answer in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
- Given instead that \(w = z\) and the real part of \(z\) is negative, find \(z\), giving your answer in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.