| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Multiplication and powers of complex numbers |
| Difficulty | Moderate -0.8 This is a straightforward Further Pure 1 question testing basic complex number operations: linear combination with conjugate, squaring a complex expression, and division by a complex number. All three parts use standard techniques (conjugate multiplication for division, expanding brackets) with no conceptual difficulty or problem-solving required. While FP1 content, these are routine manipulations that are easier than average A-level questions overall. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02f Convert between forms: cartesian and modulus-argument |
4 The complex number $3 - 4 \mathrm { i }$ is denoted by $z$. Giving your answers in the form $x + \mathrm { i } y$, and showing clearly how you obtain them, find\\
(i) $2 z + 5 z ^ { * }$,\\
(ii) $( z - \mathrm { i } ) ^ { 2 }$,\\
(iii) $\frac { 3 } { z }$.
\hfill \mbox{\textit{OCR FP1 2008 Q4 [8]}}