| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Year | 2020 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Geometric relationships on Argand diagram |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic complex number operations: plotting conjugates and differences on an Argand diagram, then performing algebraic manipulation (subtraction, division by conjugate, rationalizing). All steps are routine applications of standard techniques with no problem-solving insight required. While it's Further Maths content, the operations themselves are mechanical and below average difficulty even for that level. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (a) | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | z * reflection in Re axis |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (b) | DR |
| Answer | Marks |
|---|---|
| 5 5 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | × top and bottom by 1 + 2i |
Question 2:
2 | (a) | B1
B1
[2] | 1.1
1.1 | z * reflection in Re axis
1
z − z forming parallelogram
2 1
2 | (b) | DR
z −z 2−i (2−i)(1+2i)
2 1 = =
z * 1−2i (1−2i)(1+2i)
1
4 3
= + i
5 5 | M1
A1
[2] | 1.1
1.1 | × top and bottom by 1 + 2i
4+3i
condone
52 Fig. 2 shows two complex numbers $z _ { 1 }$ and $z _ { 2 }$ represented on an Argand diagram.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{55a4a9f1-ed86-44bb-8759-dfee0b66f56d-2_985_997_781_239}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
\begin{enumerate}[label=(\alph*)]
\item On the copy of Fig. 2 in the Printed Answer Booklet, mark points representing each of the following complex numbers.
\begin{itemize}
\item $\mathrm { Z } _ { 1 } { } ^ { * }$
\item $z _ { 2 } - z _ { 1 }$
\item In this question you must show detailed reasoning.
\end{itemize}
In the case where $z _ { 1 } = 1 + 2 \mathrm { i }$ and $z _ { 2 } = 3 + \mathrm { i }$, find $\frac { z _ { 2 } - z _ { 1 } } { z _ { 1 } ^ { * } }$ in the form $a + \mathrm { i } b$, where $a$ and $b$ are real numbers.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2020 Q2 [4]}}