| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2013 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question on complex loci requiring standard techniques: verification by substitution, sketching a circle and half-line, and finding a second intersection using geometric symmetry or simple algebra. While it involves FP2 content, the individual steps are routine with no novel problem-solving required. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
Two loci, $L_1$ and $L_2$, in an Argand diagram are given by
$$L_1 : |z + 6 - 5\text{i}| = 4\sqrt{2}$$
$$L_2 : \arg(z + \text{i}) = \frac{3\pi}{4}$$
The point $P$ represents the complex number $-2 + \text{i}$.
\begin{enumerate}[label=(\alph*)]
\item Verify that the point $P$ is a point of intersection of $L_1$ and $L_2$. [2 marks]
\item Sketch $L_1$ and $L_2$ on one Argand diagram. [6 marks]
\item The point $Q$ is also a point of intersection of $L_1$ and $L_2$. Find the complex number that is represented by $Q$. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2013 Q2 [10]}}