| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | February |
| Marks | 7 |
| Topic | Complex Numbers Arithmetic |
| Type | Geometric properties using complex numbers |
| Difficulty | Standard +0.8 This is a Further Maths complex numbers question requiring geometric understanding of rotation in the Argand diagram. Part (a) needs distance calculation (straightforward). Part (b) requires recognizing that rotating the side vector by ±90° gives the other vertices—a non-trivial insight that goes beyond routine manipulation, though it's a standard FM technique once learned. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02k Argand diagrams: geometric interpretation |
In an Argand diagram the points representing the numbers $2 + 3i$ and $1 - i$ are two adjacent vertices of a square, $S$.
\begin{enumerate}[label=(\alph*)]
\item Find the area of $S$. [3]
\item Find all the possible pairs of numbers represented by the other two vertices of $S$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q7 [7]}}