| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring students to write equations for a circle and half-line from an Argand diagram, then find their intersection. While it involves multiple parts, each step is routine: identifying loci from a diagram, using set notation, and solving simultaneous equations in complex form. The algebraic manipulation is standard for Further Maths students, making this slightly easier than average. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines4.02p Set notation: for loci |
11.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0e7cab3d-c1e6-4420-93b4-eca5af704432-10_766_791_283_701}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
The Argand diagram, shown in Figure 1, shows a circle $C$ and a half-line $l$.
\begin{enumerate}[label=(\alph*)]
\item Write down the equation of the locus of points represented in the complex plane by
\begin{enumerate}[label=(\roman*)]
\item the circle $C$,
\item the half-line $l$.
\end{enumerate}\item Use set notation to describe the set of points that lie on both $C$ and $l$.
\item Find the complex numbers that lie on both $C$ and $l$, giving your answers in the form $a + \mathrm { i } b$, where $a , b \in \mathbb { R }$.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q11 [6]}}