- The point \(P\) represents a complex number \(z\) on an Argand diagram such that
$$| z - 6 \mathrm { i } | = 2 | z - 3 |$$
- Show that, as \(z\) varies, the locus of \(P\) is a circle, stating the radius and the coordinates of the centre of this circle.
The point \(Q\) represents a complex number \(z\) on an Argand diagram such that
$$\arg ( z - 6 ) = - \frac { 3 \pi } { 4 }$$
- Sketch, on the same Argand diagram, the locus of \(P\) and the locus of \(Q\) as \(z\) varies.
- Find the complex number for which both \(| z - 6 \mathrm { i } | = 2 | z - 3 |\) and \(\arg ( z - 6 ) = - \frac { 3 \pi } { 4 }\)