- The transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac { z - \mathrm { i } } { z + 1 } \quad z \neq - 1$$
Given that \(T\) maps the imaginary axis in the \(z\)-plane to the circle \(C\) in the \(w\)-plane, determine (i) the coordinates of the centre of \(C\)
(ii) the radius of \(C\)