- A circle \(C\) in the complex plane is defined by the locus of points satisfying
$$| z - 3 i | = 2 | z |$$
- Determine a Cartesian equation for \(C\), giving your answer in simplest form.
- On an Argand diagram, shade the region defined by
$$\{ z \in \mathbb { C } : | z - 3 \mathrm { i } | > 2 | z | \}$$
(ii) The transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = z ^ { 3 }$$
- Describe the geometric effect of \(T\).
The region \(R\) in the \(z\)-plane is given by
$$\left\{ z \in \mathbb { C } : 0 < \arg z < \frac { \pi } { 4 } \right\}$$
- On a different Argand diagram, sketch the image of \(R\) under \(T\).