| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | February |
| Marks | 7 |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths complex numbers question requiring basic understanding of modulus and argument. Part (i) involves sketching a circle and a ray, both standard loci. Part (ii) requires finding their intersection using z = r(cos θ + i sin θ) with r=2 and θ=π/4, giving z = √2 + i√2. This is routine application of definitions with no problem-solving or novel insight required, making it easier than average. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
In an Argand diagram the loci $C_1$ and $C_2$ are given by
$$|z| = 2 \quad \text{and} \quad \arg z = \frac{1}{4}\pi$$
respectively.
\begin{enumerate}[label=(\roman*)]
\item Sketch, on a single Argand diagram, the loci $C_1$ and $C_2$. [5]
\item Hence find, in the form $x + iy$, the complex number representing the point of intersection of $C_1$ and $C_2$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q6 [7]}}