| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core (Further Pure Core) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Modulus-argument form conversion |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question requiring standard conversions between Cartesian and modulus-argument forms, followed by division using the quotient rule. While it involves multiple steps and exact values (requiring knowledge of special angles), these are routine techniques for Further Maths students with no problem-solving or novel insight required. Slightly easier than average due to its mechanical nature. |
| Spec | 4.02b Express complex numbers: cartesian and modulus-argument forms4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z)4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | DR |
| Answer | Marks |
|---|---|
| 4 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 1.1 | |
| 1.1 | Must see some reasoning for arg(z) | |
| 3 | (b) | DR |
| Answer | Marks |
|---|---|
| 2 | B1 |
| Answer | Marks |
|---|---|
| [4] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | ( z ) |
Question 3:
3 | (a) | DR
z = 8
1
3
a r g ( z ) =
1
4 | B1
E1
[2] | 1.1
1.1 | Must see some reasoning for arg(z)
3 | (b) | DR
z 8
1 = = 2
z 2
2
( z ) 3 7
a r g 1 = − =
z 4 6 1 2
2
z ( 7 7)
so 1 = 2 cos +isin
z 12 12
2 | B1
M1
A1
B1
[4] | 1.1
1.1
1.1
1.1 | ( z )
a r g 1 = a r g ( z ) − a r g ( z ) used
1 2
z
23 In this question you must show detailed reasoning.\\
The complex numbers $z _ { 1 }$ and $z _ { 2 }$ are given by $z _ { 1 } = - 2 + 2 i$ and $z _ { 2 } = 2 \left( \cos \frac { 1 } { 6 } \pi + i \sin \frac { 1 } { 6 } \pi \right)$.
\begin{enumerate}[label=(\alph*)]
\item Find the modulus and argument of $z _ { 1 }$.
\item Hence express $\frac { z _ { 1 } } { z _ { 2 } }$ in exact modulus-argument form.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core 2021 Q3 [6]}}