| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex transformations and mappings |
| Difficulty | Standard +0.8 This FP2 question requires understanding of loci in the Argand diagram, solving simultaneous geometric conditions, and proving that a transformation maps one locus to another. Part (a) is routine (perpendicular bisector), part (b) requires solving a circle-line intersection algebraically, but part (c) demands substitution of w=30/z, manipulation to find the image locus, and proving it's a circle—this multi-step transformation proof with algebraic manipulation elevates it above standard A-level but remains accessible to strong FP2 students. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
A complex number $z$ is represented by the point $P$ in the Argand diagram.
\begin{enumerate}[label=(\alph*)]
\item Given that $|z - 6| = |z|$, sketch the locus of $P$. [2]
\item Find the complex numbers $z$ which satisfy both $|z - 6| = |z|$ and $|z - 3 - 4i| = 5$. [3]
\end{enumerate}
The transformation $T$ from the $z$-plane to the $w$-plane is given by $w = \frac{30}{z}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that $T$ maps $|z - 6| = |z|$ onto a circle in the $w$-plane and give the cartesian equation of this circle. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q6 [10]}}