| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Region shading with multiple inequalities |
| Difficulty | Standard +0.3 This is a straightforward locus question requiring recognition that |z - 6i| = 3 is a circle centered at 6i with radius 3, then finding maximum |z| (distance from origin = 9) and maximum arg z using basic geometry/trigonometry. Standard FP2 material with minimal problem-solving required beyond applying definitions. |
| 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
$$| z - 6 \mathrm { i } | = 3$$
\item It is given that $z$ satisfies the equation $| z - 6 \mathrm { i } | = 3$.
\begin{enumerate}[label=(\roman*)]
\item Write down the greatest possible value of $| z |$.
\item Find the greatest possible value of $\arg z$, giving your answer in the form $p \pi$, where $- 1 < p \leqslant 1$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2013 Q1 [7]}}