IAL 2022 Oct Q5

The transformation $T$ from the $z$ -plane to the $w$ -plane is given by

\begin{align*} w =\,& \frac{z-3\mathrm{i}}{z+2\mathrm{i}} \qquad z \neq -2\mathrm{i}\\[2mm] \end{align*}

The circle with equation $|z|=1$ in the $z$ -plane is mapped by $T$ onto the circle $C$ in the $w$ -plane.

Determine

(i) the centre of $C$ ,

(ii) the radius of $C$ .

(7)