- A complex number \(z\) is represented by the point \(P\) in an Argand diagram.
Given that
$$| z - 2 i | = | z - 3 |$$
- sketch the locus of \(P\). You do not need to find the coordinates of any intercepts.
The transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac { \mathrm { i } z } { z - 2 \mathrm { i } } \quad z \neq 2 \mathrm { i }$$
Given that \(T\) maps \(| z - 2 i | = | z - 3 |\) to a circle \(C\) in the \(w\)-plane,
- find the equation of \(C\), giving your answer in the form
$$| w - ( p + q \mathrm { i } ) | = r$$
where \(p , q\) and \(r\) are real numbers to be determined.