| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Circle equations in complex form |
| Difficulty | Easy -1.2 This is a straightforward Further Maths question testing basic complex number properties. Part (i) is direct verification using standard notation (1 mark), and part (ii) requires recognizing that |z|²=9 means |z|=3, which is a circle of radius 3—a standard locus result requiring minimal problem-solving. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02o Loci in Argand diagram: circles, half-lines |
\begin{enumerate}[label=(\roman*)]
\item By writing $z$ in the form $re^{i\theta}$, show that $zz^* = |z|^2$. [1]
\item Given that $zz^* = 9$, describe the locus of $z$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP3 Q1 [3]}}