| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Modulus and argument with operations |
| Difficulty | Moderate -0.8 This is a straightforward Further Pure 1 question testing basic complex number operations: finding reciprocals, squaring, modulus, and argument. All parts use standard algorithms with the given z = -2 + i. While FP1 content is more advanced than Core modules, these are routine manipulations requiring no problem-solving insight, making it easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
$$z = -2 + i.$$
\begin{enumerate}[label=(\alph*)]
\item Express in the form $a + ib$
\begin{enumerate}[label=(\roman*)]
\item $\frac{1}{z}$
\item $z^2$. [4]
\end{enumerate}
\item Show that $|z^2 - z| = 5\sqrt{2}$. [2]
\item Find $\arg (z^2 - z)$. [2]
\item Display $z$ and $z^2 - z$ on a single Argand diagram. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q44 [10]}}