| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex arithmetic operations |
| Difficulty | Moderate -0.5 This is a straightforward Further Maths question testing basic complex number operations: squaring a complex number, finding modulus and argument, and plotting on an Argand diagram. All parts are routine calculations with no problem-solving required. While it's FP1 content (inherently harder than C1-C4), the techniques are mechanical and well-practiced, making it slightly easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02k Argand diagrams: geometric interpretation |
1.
$$z = 2 - 3 \mathrm { i }$$
\begin{enumerate}[label=(\alph*)]
\item Show that $z ^ { 2 } = - 5 - 12 \mathrm { i }$.
Find, showing your working,
\item the value of $\left| z ^ { 2 } \right|$,
\item the value of $\arg \left( z ^ { 2 } \right)$, giving your answer in radians to 2 decimal places.
\item Show $z$ and $z ^ { 2 }$ on a single Argand diagram.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 2010 Q1 [7]}}