| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Geometric properties using complex numbers |
| Difficulty | Standard +0.8 This is a Further Maths question requiring geometric understanding of complex numbers, including rotation by 90° (multiplication by ±i) and distance calculations. Part (a) requires finding the side length using modulus, while part (b) demands systematic consideration of two cases (which diagonal) and applying complex number rotations. It goes beyond routine manipulation to require spatial reasoning and multiple solution paths, making it moderately challenging even for Further Maths students. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02l Geometrical effects: conjugate, addition, subtraction |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (a) | (2 + 3i) – (1 – i) (= ±(1 + 4i)) soi |
| Answer | Marks | Guidance |
|---|---|---|
| 1+4i | = �1 +4 | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | Either way round |
| Answer | Marks | Guidance |
|---|---|---|
| Or at 5 – 2i and 6 + 2i | A1 | |
| [4] | 3.2a | Both clearly paired and in |
| Answer | Marks |
|---|---|
| A1 | If M1M0A0A0 then add SC1 for |
Question 7:
7 | (a) | (2 + 3i) – (1 – i) (= ±(1 + 4i)) soi
17
2 2
| 1+4i| = �1 +4 | B1
M1
A1
[3] | 1.1
2.2a
1.1 | Either way round
Can be implied by vector
Or finding the square of their side
Or at 5 – 2i and 6 + 2i | A1
[4] | 3.2a | Both clearly paired and in
complex number form for final
A1 | If M1M0A0A0 then add SC1 for
any two correct vertices7 In an Argand diagram the points representing the numbers $2 + 3 \mathrm { i }$ and $1 - \mathrm { i }$ are two adjacent vertices of a square, $S$.
\begin{enumerate}[label=(\alph*)]
\item Find the area of $S$.
\item Find all the possible pairs of numbers represented by the other two vertices of $S$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 2 2019 Q7 [7]}}