| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Year | 2023 |
| Session | June |
| 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 plotting exercise requiring only basic knowledge of complex number operations (conjugate, reciprocal, addition, multiplication by i) on an Argand diagram. Given |z|=2 and a diagram showing z's position, students apply standard transformations with no problem-solving or novel insight required—purely procedural recall of geometric interpretations. |
| 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 |
|---|---|
| 5 | B1 |
| Answer | Marks |
|---|---|
| [4] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | z*: reflection of z in Re axis |
Question 5:
5 | B1
B1
B1
B1
[4] | 1.1
1.1
1.1
1.1 | z*: reflection of z in Re axis
1 + z: 1 unit to right of z
1/z: arg = − arg z (must be < 45), ½ unit from O
iz: rotation of z 90anticlockwise about O
Give mark if intention is clear.5 The Argand diagram below shows the points representing 1 and $z$, where $| z | = 2$.\\
\includegraphics[max width=\textwidth, alt={}, center]{26cec6f9-78a7-4f0b-969a-13ad02510c25-3_577_595_312_242}
Mark the points representing the following complex numbers on the copy of the diagram in the Printed Answer Booklet, labelling them clearly.
\begin{itemize}
\item $\mathrm { Z } ^ { * }$
\item $\frac { 1 } { z }$
\item $1 + z$
\item iz
\end{itemize}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2023 Q5 [4]}}