- A curve \(C\) in the complex plane is described by the equation
$$| z - 1 - 8 i | = 3 | z - 1 |$$
- Show that \(C\) is a circle, and find its centre and radius.
- Using the answer to part (a), determine whether \(z = 3 - 3 \mathrm { i }\) satisfies the inequality
$$| z - 1 - 8 i | \geqslant 3 | z - 1 |$$
- Shade, on an Argand diagram, the set of points that satisfies both
$$| z - 1 - 8 i | \geqslant 3 | z - 1 | \quad \text { and } \quad 0 \leqslant \arg ( z + i ) \leqslant \frac { \pi } { 4 }$$