IAL 2021 June Q2

The transformation $T$ from the $z$-plane, where $z = x + iy$, to the $w$-plane, where $w = u + iv$, is given by

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 $C$.