6 In an Argand diagram the points \(A\) and \(B\) represent the complex numbers \(5 + 4 \mathrm { i }\) and \(1 + 2 \mathrm { i }\) respectively.
- Given that \(A\) and \(B\) are the ends of a diameter of a circle \(C\), find the equation of \(C\) in complex number form.
The perpendicular bisector of \(A B\) is denoted by \(l\).
- Sketch \(C\) and \(l\) on a single Argand diagram.
- Find the complex numbers represented by the points of intersection of \(C\) and \(l\).