| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Optimization of modulus on loci |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring recognition that |z - (4-3i)| = 5 is a circle, sketching it, finding the intersection with the positive real axis (arg z = 0), and calculating a modulus. All steps are routine applications of standard locus definitions with no novel problem-solving required. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
1
\begin{enumerate}[label=(\alph*)]
\item Sketch on an Argand diagram the locus of points satisfying the equation
$$| z - 4 + 3 \mathrm { i } | = 5$$
\item \begin{enumerate}[label=(\roman*)]
\item Indicate on your diagram the point $P$ representing $z _ { 1 }$, where both
$$\left| z _ { 1 } - 4 + 3 \mathrm { i } \right| = 5 \quad \text { and } \quad \arg z _ { 1 } = 0$$
\item Find the value of $\left| z _ { 1 } \right|$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2011 Q1 [5]}}