- A transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac { 1 - 3 z } { z + 2 i } \quad z \neq - 2 i$$
The circle with equation \(| z + \mathrm { i } | = 3\) is mapped by \(T\) onto the circle \(C\).
- Show that the equation for \(C\) can be written as
$$3 | w + 3 | = | 1 + ( 3 - w ) \mathrm { i } |$$
- Hence find
- a Cartesian equation for \(C\),
- the centre and radius of \(C\).