| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Modulus and argument with operations |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing basic complex number operations: modulus calculation, complex division using conjugates, and argument finding. While it requires multiple steps and the 'hence' structure adds mild problem-solving, each individual technique is standard and the connection between parts is clear. The division simplifies nicely to kz form, making part (c) trivial. Slightly above average difficulty due to being Further Maths content, but routine for that level. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z) |
\begin{enumerate}
\item In this question you must show all stages of your working.
\end{enumerate}
\section*{Solutions relying entirely on calculator technology are not acceptable.}
The complex number $z$ is defined by
$$2 = - 3 + 4 i$$
(a) Determine $\left| z ^ { 2 } - 3 \right|$\\
(b) Express $\frac { 50 } { z ^ { * } }$ in the form $k z$, where $k$ is a positive integer.\\
(c) Hence find the value of $\arg \left( \frac { 50 } { z ^ { * } } \right)$
Give your answer in radians to 3 significant figures.
\hfill \mbox{\textit{Edexcel F1 2024 Q4 [8]}}