| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Geometric properties using complex numbers |
| Difficulty | Moderate -0.3 This is a straightforward FP1 complex numbers question testing basic skills: modulus calculation (routine), plotting on Argand diagram (trivial), proving triangle properties using distance/dot product (standard technique), and finding argument of quotient (standard). The proof in part (c) requires multiple steps but uses well-practiced methods. Slightly easier than average A-level due to computational simplicity and standard techniques, though the 10-mark allocation and proof element prevent it from being significantly below average. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02k Argand diagrams: geometric interpretation |
Given that $z = 3 + 4i$ and $w = -1 + 7i$.
\begin{enumerate}[label=(\alph*)]
\item find $|w|$. [1]
\end{enumerate}
The complex numbers $z$ and $w$ are represented by the points $A$ and $B$ on an Argand diagram.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show points $A$ and $B$ on an Argand diagram. [1]
\item Prove that $\triangle OAB$ is an isosceles right-angled triangle. [5]
\item Find the exact value of $\arg \left( \frac{z}{w} \right)$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q6 [10]}}