| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Topic | Complex Numbers Argand & Loci |
| Type | Single locus sketching |
| Difficulty | Moderate -0.8 Part (a) is direct recall of a standard locus (circle with center 2, radius 2). Part (b) requires converting from modulus-argument form to Cartesian form, which is a routine A-level technique involving basic trigonometry. Both parts are straightforward applications of fundamental complex number concepts with no problem-solving required. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02l Geometrical effects: conjugate, addition, subtraction |
3.\\
\begin{enumerate}[label=(\alph*)]
\item Sketch on the Argand diagram below the locus of points satisfying the equation $| z - 2 | = 2$.\\
\includegraphics[max width=\textwidth, alt={}, center]{ace492d8-1dd0-401e-af74-505ca19d5e9c-08_1260_1303_260_468}
\item Given that $| z - 2 | = 2$ and $\arg ( z - 2 ) = - \frac { \pi } { 3 }$, express $z$ in the form $a + b i$ where $a , b \in \mathbb { R }$.\\[0pt]
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\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q3 [5]}}