| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a straightforward FP1 loci question requiring standard techniques: recognizing |z - 2i| = 2 as a circle centered at 2i with radius 2, and |z + 1| = |z + i| as the perpendicular bisector of -1 and -i. Finding intersections by inspection from the sketch is routine. While it involves complex number loci (an FP1 topic), the question requires only pattern recognition and basic geometric reasoning, making it slightly easier than average overall. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
The loci $C_1$ and $C_2$ are given by
$$|z - 2i| = 2 \quad \text{and} \quad |z + 1| = |z + i|$$
respectively.
\begin{enumerate}[label=(\roman*)]
\item Sketch, on a single Argand diagram, the loci $C_1$ and $C_2$. [5]
\item Hence write down the complex numbers represented by the points of intersection of $C_1$ and $C_2$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 Q6 [7]}}