10. The point \(P\) represents a complex number \(z\) on an Argand diagram such that
$$| z - 3 | = 2 | z |$$
- Show that, as \(z\) varies, the locus of \(P\) is a circle, and give the coordinates of the centre and the radius of the circle.(5)
The point \(Q\) represents a complex number \(z\) on an Argand diagram such that
$$| z + 3 | = | z - i \sqrt { } 3 |$$
- Sketch, on the same Argand diagram, the locus of \(P\) and the locus of \(Q\) as \(z\) varies.(5)
- On your diagram shade the region which satisfies
$$| z - 3 | \geq 2 | z | \text { and } | z + 3 | \geq | z - i \sqrt { } 3 |$$