8. The point \(P\) represents a complex number \(z\) on an Argand diagram, where
$$| z - 6 + 3 i | = 3 | z + 2 - i |$$
- Show that the locus of \(P\) is a circle, giving the coordinates of the centre and the radius of this circle.
The point \(Q\) represents a complex number \(z\) on an Argand diagram, where
$$\tan [ \arg ( z + 6 ) ] = \frac { 1 } { 2 }$$
- On the same Argand diagram, sketch the locus of \(P\) and the locus of \(Q\).
- On your diagram, shade the region which satisfies both
$$| z - 6 + 3 \mathrm { i } | > 3 | z + 2 - \mathrm { i } | \text { and } \tan [ \arg ( z + 6 ) ] > \frac { 1 } { 2 }$$
(2)(Total 14 marks)