| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Topic | Complex Numbers Argand & Loci |
| Type | Area calculations in complex plane |
| Difficulty | Standard +0.8 This is a Further Maths question requiring geometric understanding of complex numbers and rotation in the Argand diagram. Part (a) is straightforward (distance formula), but part (b) requires recognizing that there are two possible squares and applying rotation by ±90° about appropriate centers—a non-trivial multi-step problem requiring spatial reasoning beyond standard exercises. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02k Argand diagrams: geometric interpretation4.02m Geometrical effects: multiplication and division |
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{OCR Further Pure Core 2 2021 Q4 [7]}}