| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Topic | Complex Numbers Argand & Loci |
| Type | Region shading with multiple inequalities |
| Difficulty | Moderate -0.3 This is a standard complex numbers loci question requiring students to sketch a circle centered at origin with radius 4 and a half-line from -4i at angle π/4, then shade the intersection region. While it requires understanding of modulus and argument, it's a routine textbook exercise with no novel problem-solving or proof required, making it slightly easier than average. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
2 (i) On a single Argand diagram, sketch and clearly label each of the following loci:
\begin{enumerate}[label=(\alph*)]
\item $| z | = 4$,
\item $\quad \arg ( z + 4 \mathrm { i } ) = \frac { 1 } { 4 } \pi$.\\
(ii) On the same Argand diagram, shade the region $R$ defined by the inequalities
$$| z | \leqslant 4 \quad \text { and } \quad 0 \leqslant \arg ( z + 4 i ) \leqslant \frac { 1 } { 4 } \pi$$
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q2}}