7 The loci \(C _ { 1 }\) and \(C _ { 2 }\) are given by \(| z - 3 - 4 \mathrm { i } | = 4\) and \(| z | = | z - 8 \mathrm { i } |\) respectively.
- Sketch, on a single Argand diagram, the loci \(C _ { 1 }\) and \(C _ { 2 }\).
- Hence find the complex numbers represented by the points of intersection of \(C _ { 1 }\) and \(C _ { 2 }\).
- Indicate, by shading, the region of the Argand diagram for which
$$| z - 3 - 4 i | \leqslant 4 \text { and } | z | \geqslant | z - 8 i | .$$