2. The transformation \(T\) from the \(z\)-plane, where \(z = x + \mathrm { i } y\), to the \(w\)-plane, where \(w = u + \mathrm { i } v\), is given by $$w = \frac { z + 2 } { z - \mathrm { i } } \quad z \neq \mathrm { i }$$ The transformation \(T\) maps the circle \(| z | = 2\) in the \(z\)-plane onto a circle \(C\) in the \(w\)-plane.
Find (i) the centre of \(C\),
(ii) the radius of \(C\).