| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | January |
| 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 arithmetic. Part (i) is direct multiplication requiring only FOIL and i²=-1. Part (ii) uses the conjugate method, made easier by the hint 'hence' linking to part (i). Both are standard textbook exercises with no problem-solving or insight required, though the Further Maths context places it slightly above the easiest A-level questions. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
| Answer | Marks | Guidance |
|---|---|---|
| \(2 + 16i - i - 8i^2\) | M1 A1 | Attempt to multiply correctly; Obtain correct answer |
| \(10 + 15i\) | M1 A1 | Multiply numerator & denominator by conjugate; Obtain denominator 5 |
| \(\frac{1}{5}(10 + 15i)\) or \(2 + 3i\) | A1ft | Their part (i) or \(10 + 15i\) derived again / 5 |
$2 + 16i - i - 8i^2$ | M1 A1 | Attempt to multiply correctly; Obtain correct answer
$10 + 15i$ | M1 A1 | Multiply numerator & denominator by conjugate; Obtain denominator 5
$\frac{1}{5}(10 + 15i)$ or $2 + 3i$ | A1ft | Their part (i) or $10 + 15i$ derived again / 51 (i) Express $( 1 + 8 i ) ( 2 - i )$ in the form $x + i y$, showing clearly how you obtain your answer.\\
(ii) Hence express $\frac { 1 + 8 i } { 2 + i }$ in the form $x + i y$.
\hfill \mbox{\textit{OCR FP1 2006 Q1 [5]}}