5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d0194d2-7958-4699-9c5c-02e815ac433c-18_510_714_251_689}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows an Argand diagram.
The set of points, \(A\), that lies within the shaded region, including its boundaries, is defined by
$$A = \{ z : p \leqslant \arg ( z ) \leqslant q \} \cap \{ z : | z | \leqslant r \}$$
where \(p , q\) and \(r\) are positive constants.
- Write down the values of \(p , q\) and \(r\).
Given that \(w = - 2 \sqrt { 3 } + 2 \mathrm { i }\) and \(\mathrm { z } \in A\),
- find the maximum value of \(| w - z | ^ { 2 }\) giving your answer in an exact simplified form.