- A curve \(C\) is described by the equation
$$| z - 9 + 12 i | = 2 | z |$$
- Show that \(C\) is a circle, and find its centre and radius.
- Sketch \(C\) on an Argand diagram.
Given that \(w\) lies on \(C\),
- find the largest value of \(a\) and the smallest value of \(b\) that must satisfy
$$a \leqslant \operatorname { Re } ( w ) \leqslant b$$