- A transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac { z } { z + 3 \mathrm { i } } , \quad z \neq - 3 \mathrm { i }$$
The circle with equation \(| z | = 2\) is mapped by \(T\) onto the curve \(C\).
- Show that \(C\) is a circle.
- Find the centre and radius of \(C\).
The region \(| z | \leqslant 2\) in the \(z\)-plane is mapped by \(T\) onto the region \(R\) in the \(w\)-plane.
- Shade the region \(R\) on an Argand diagram.