- The locus \(C\) is given by
$$| z - 4 | = 4$$
The locus \(D\) is given by
$$\arg z = \frac { \pi } { 3 }$$
- Sketch, on the same Argand diagram, the locus \(C\) and the locus \(D\)
The set of points \(A\) is defined by
$$A = \{ z \in \mathbb { C } : | z - 4 | \leqslant 4 \} \cap \left\{ z \in \mathbb { C } : 0 \leqslant \arg z \leqslant \frac { \pi } { 3 } \right\}$$
- Show, by shading on your Argand diagram, the set of points \(A\)
- Find the area of the region defined by \(A\), giving your answer in the form \(p \pi + q \sqrt { 3 }\) where \(p\) and \(q\) are constants to be determined.