8. A complex number \(z\) is represented by the point \(P\) on an Argand diagram.
- Given that \(| z | = 1\), sketch the locus of \(P\).
The transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac { z + 7 \mathrm { i } } { z - 2 \mathrm { i } }$$
- Show that \(T\) maps \(| z | = 1\) onto a circle in the \(w\)-plane.
- Show that this circle has its centre at \(w = - 5\) and find its radius.