9. (a) The point \(P\) represents a complex number \(z\) in an Argand diagram. Given that
$$| z - 2 \mathrm { i } | = 2 | z + \mathrm { i } |$$
- find a cartesian equation for the locus of \(P\), simplifying your answer.
- sketch the locus of \(P\).
(b) A transformation \(T\) from the \(z\)-plane to the \(w\)-plane is a translation \(- 7 + 11 \mathrm { i }\) followed by an enlargement with centre the origin and scale factor 3 .
Write down the transformation \(T\) in the form
$$w = a z + b , \quad a , b \in \mathbb { C }$$
[P6 June 2002 Qn 3]