5 Throughout this question the use of a calculator is not permitted.
The complex numbers $w$ and $z$ satisfy the relation

$$w = \frac { z + \mathrm { i } } { \mathrm { i } z + 2 }$$

(i) Given that $z = 1 + \mathrm { i }$, find $w$, giving your answer in the form $x + \mathrm { i } y$, where $x$ and $y$ are real.\\
(ii) 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.

\hfill \mbox{\textit{CAIE P3 2014 Q5}}