| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex arithmetic operations |
| Difficulty | Moderate -0.3 This is a straightforward multi-part complex numbers question requiring routine techniques: multiplying complex numbers, finding argument and modulus using standard formulas, and calculating distance. All parts are standard FP1 exercises with no novel insight required, making it slightly easier than average A-level difficulty. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
Given that $z = 1 + \sqrt{3}i$ and that $\frac{w}{z} = 2 + 2i$, find
\begin{enumerate}[label=(\alph*)]
\item $w$ in the form $a + ib$, where $a, b \in \mathbb{R}$, [3]
\item the argument of $w$, [2]
\item the exact value for the modulus of $w$. [2]
\end{enumerate}
On an Argand diagram, the point $A$ represents $z$ and the point $B$ represents $w$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Draw the Argand diagram, showing the points $A$ and $B$. [2]
\item Find the distance $AB$, giving your answer as a simplified surd. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q19 [11]}}