Question 8 - A-Level Maths

Fig. 8 shows an Argand diagram. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{df275813-15de-496f-9742-427a9e03f431-3_892_899_1048_664} \captionsetup{labelformat=empty} \caption{Fig. 8}
\end{figure}
1. Write down the equation of the locus represented by the circumference of circle B.
2. Write down the two inequalities that define the shaded region between, but not including, circles A and B.
1. Draw an Argand diagram to show the region where $$\frac { \pi } { 4 } < \arg ( z - ( 2 + \mathrm { j } ) ) < \frac { 3 \pi } { 4 }$$
2. Determine whether the point $43 + 47 \mathrm { j }$ lies within this region.