| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | February |
| Marks | 4 |
| Topic | Complex Numbers Argand & Loci |
| Type | Perpendicular bisector locus |
| Difficulty | Moderate -0.3 This is a straightforward loci question requiring students to recognize that |z + i| = |z - 2i| represents the perpendicular bisector of two points, then find its equation. The inequality determines which half-plane to shade. While it involves complex numbers (a Further Maths topic), the geometric interpretation and algebraic manipulation are routine, making it slightly easier than an average A-level question. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
A locus $C_1$ is defined by $C_1 = \{z : |z + i| \leq |z - 2i|\}$.
\begin{enumerate}[label=(\roman*)]
\item Indicate by shading on the Argand diagram below the region representing $C_1$.
[2]
\includegraphics{figure_8}
\item Find the cartesian equation of the boundary line of the region representing $C_1$, giving your answer in the form $ax + by + c = 0$.
[2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2025 Q8 [4]}}