| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 7 |
| 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 FP1 question testing basic complex number operations: addition, multiplication with conjugates, and finding reciprocals. All three parts are routine calculations requiring only direct application of standard techniques (conjugate definition, multiplication of complex numbers, rationalizing denominators). While FP1 content is more advanced than core A-level, these are foundational exercises within the module with no problem-solving or insight required. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
The complex numbers $2 + 3i$ and $4 - i$ are denoted by $z$ and $w$ respectively. Express each of the following in the form $x + iy$, showing clearly how you obtain your answers.
\begin{enumerate}[label=(\roman*)]
\item $z + 5w$, [2]
\item $z*w$, where $z*$ is the complex conjugate of $z$, [3]
\item $\frac{1}{w}$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 Q3 [7]}}