| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic complex number operations: addition/scalar multiplication and division by multiplying by the conjugate. Both are routine procedures with no problem-solving required. While it's FP1, these are foundational skills, making it easier than average even for A-level standards. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
| Answer | Marks | Guidance |
|---|---|---|
| \(21 + 11i\) | B1 | Real part correct |
| B1 | Imaginary part correct |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | Multiply by conjugate of denominator or find a pair of simultaneous equations | |
| \(26 - 29i\) | A1 | Obtain correct numerator or real part |
| \(\frac{26}{41} - \frac{29}{41}i\) | A1 | Obtain correct denominator or imaginary part |
## Question 1:
### Part (i)
$21 + 11i$ | B1 | Real part correct
| B1 | Imaginary part correct
**[2]**
### Part (ii)
| M1 | Multiply by conjugate of denominator or find a pair of simultaneous equations
$26 - 29i$ | A1 | Obtain correct numerator or real part
$\frac{26}{41} - \frac{29}{41}i$ | A1 | Obtain correct denominator or imaginary part
**[3]**
---1 The complex numbers $z$ and $w$ are given by $z = 6 - \mathrm { i }$ and $w = 5 + 4 \mathrm { i }$. Giving your answers in the form $x + \mathrm { i } y$ and showing clearly how you obtain them, find\\
(i) $z + 3 w$,\\
(ii) $\frac { Z } { W }$.
\hfill \mbox{\textit{OCR FP1 2012 Q1 [5]}}