IAL 2022 June Q3

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

\begin{align*} w =\,& \frac{z}{z + 4\mathrm{i}} \qquad z \neq -4\mathrm{i}\\[2mm] \end{align*}

The circle with equation $|z| = 3$ is mapped by $T$ onto the circle $C$

Determine

(i) a Cartesian equation of $C$

(ii) the centre and radius of $C$

(8)