5 The locus of points, \(L\), satisfies the equation
$$| z - 2 + 4 \mathrm { i } | = | z |$$
- Sketch \(L\) on the Argand diagram below.
- The locus \(L\) cuts the real axis at \(A\) and the imaginary axis at \(B\).
- Show that the complex number represented by \(C\), the midpoint of \(A B\), is
$$\frac { 5 } { 2 } - \frac { 5 } { 4 } \mathrm { i }$$
- The point \(O\) is the origin of the Argand diagram. Find the equation of the circle that passes through the points \(O , A\) and \(B\), giving your answer in the form \(| z - \alpha | = k\).
[0pt]
[2 marks]
\section*{(a)}
\includegraphics[max width=\textwidth, alt={}]{bc3aaed2-4aef-4aec-b657-098b1e581e55-10_1173_1242_1217_463}