5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d7dcb9f-510c-42c7-bcac-6d6ab3ed6468-12_584_830_246_639}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows an Argand diagram.
The set \(P\), of points that lie within the shaded region including its boundaries, is defined by
$$P = \{ z \in \mathbb { C } : a \leqslant | z + b + c \mathrm { i } | \leqslant d \}$$
where \(a\), \(b\), \(c\) and \(d\) are integers.
- Write down the values of \(a , b , c\) and \(d\).
The set \(Q\) is defined by
$$Q = \{ z \in \mathbb { C } : a \leqslant | z + b + c \mathrm { i } | \leqslant d \} \cap \{ z \in \mathbb { C } : | z - \mathrm { i } | \leqslant | z - 3 \mathrm { i } | \}$$
- Determine the exact area of the region defined by \(Q\), giving your answer in simplest form.