4. A complex number \(z\) is represented by the point \(P\) in an Argand diagram. Given that
$$| z + i | = 1$$
- sketch the locus of \(P\).
The transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac { 3 \mathrm { i } z - 2 } { z + \mathrm { i } } , \quad z \neq - \mathrm { i }$$
- Given that \(T\) maps \(| z + i | = 1\) to a circle \(C\) in the \(w\)-plane, find a cartesian equation of \(C\).