| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus modulus/argument |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths AS question testing basic complex number conversions and division. Part (i) is direct application of r(cos θ + i sin θ) with standard angle values, and part (ii) requires multiplying by the conjugate—both routine procedures with no problem-solving insight needed. While Further Maths content, the mechanical nature and low mark allocation place it below average difficulty. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02f Convert between forms: cartesian and modulus-argument |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | (cid:167) (cid:83) (cid:83)(cid:183) |
| Answer | Marks |
|---|---|
| = 2(cid:14)2 3i | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 1.1 | |
| 1.1 | May be implied | |
| or exact equivalent | a = 2, b = 2 3 | |
| 1 | (ii) | (cid:11) (cid:12) |
| Answer | Marks |
|---|---|
| (cid:32) 3(cid:14)1 (cid:14) 3(cid:16)1 i | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | N |
Question 1:
1 | (i) | (cid:167) (cid:83) (cid:83)(cid:183)
z (cid:32)4(cid:168)cos (cid:14)isin (cid:184)
2 (cid:169) 3 3(cid:185)
= 2(cid:14)2 3i | M1
A1
[2] | 1.1
1.1 | May be implied
or exact equivalent | a = 2, b = 2 3
1 | (ii) | (cid:11) (cid:12)
2(cid:14)2 3i (cid:11)1(cid:16)i(cid:12)
z
2 (cid:32)
z (cid:11)1(cid:14)i(cid:12)(cid:11)1(cid:16)i(cid:12)
1
(cid:11) (cid:12) (cid:11) (cid:12)
2(cid:14)2 3 (cid:14) 2 3(cid:16)2 i
(cid:32)
2
(cid:11) (cid:12) (cid:11) (cid:12)
(cid:32) 3(cid:14)1 (cid:14) 3(cid:16)1 i | M1
A1 FT
[2] | 1.1a
M
1.1 | N
FT their z
E2
Must be simplifiedThe complex number $z_1$ is $1+ i$ and the complex number $z_2$ has modulus 4 and argument $\frac{\pi}{3}$.
\begin{enumerate}[label=(\roman*)]
\item Express $z_2$ in the form $a + bi$, giving $a$ and $b$ in exact form. [2]
\item Express $\frac{z_2}{z_1}$ in the form $c + di$, giving $c$ and $d$ in exact form. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS Q1 [4]}}