| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Circle of Apollonius locus |
| Difficulty | Standard +0.3 This is a straightforward FP2 question testing standard locus techniques and transformations. Part (a) requires algebraic manipulation of modulus equations to find a circle (Apollonius circle), which is routine for FP2 students. Part (b) is direct application of combining transformations. Both parts are textbook exercises requiring recall and standard methods rather than problem-solving or insight. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02m Geometrical effects: multiplication and division |
\begin{enumerate}[label=(\alph*)]
\item The point $P$ represents a complex number $z$ in an Argand diagram. Given that
$$|z - 2i| = 2|z + i|,$$
\begin{enumerate}[label=(\roman*)]
\item find a cartesian equation for the locus of $P$, simplifying your answer. [2]
\item sketch the locus of $P$. [3]
\end{enumerate}
\item A transformation $T$ from the $z$-plane to the $w$-plane is a translation $-7 + 11i$ followed by an enlargement with centre the origin and scale factor $3$.
Write down the transformation $T$ in the form
$$w = az + b, \quad a, b \in \mathbb{C}.$$ [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q9 [7]}}