12.
Fig. 9 shows a sketch of the region OPQ of the Argand diagram defined by
$$\{ z : | z | \leqslant 4 \sqrt { 2 } \} \cap \left\{ z : \frac { 1 } { 4 } \pi \leqslant \arg z \leqslant \frac { 1 } { 3 } \pi \right\} .$$
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5739a9ae-d1ed-4c9d-a912-587ece5e9627-21_547_517_447_733}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\end{figure}
- Find, in modulus-argument form, the complex number represented by the point P .
- Find, in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are exact real numbers, the complex number represented by the point Q .
- In this question you must show detailed reasoning.
Determine whether the points representing the complex numbers
- \(3 + 5 \mathrm { i }\)
- \(5.5 ( \cos 0.8 + \mathrm { i } \sin 0.8 )\)
lie within this region.