6. The complex number \(z\) on an Argand diagram is represented by the point \(P\) where
$$| z + 1 - 13 i | = 3 | z - 7 - 5 i |$$
Given that the locus of \(P\) is a circle,
- determine the centre and radius of this circle.
The complex number \(w\), on the same Argand diagram, is represented by the point \(Q\), where
$$\arg ( w - 8 - 6 \mathrm { i } ) = - \frac { 3 \pi } { 4 }$$
Given that the locus of \(P\) intersects the locus of \(Q\) at the point \(R\),
- determine the complex number representing \(R\).