| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Parameter from argument condition |
| Difficulty | Standard +0.3 This is a standard FP1 complex numbers question testing modulus and argument calculations. Part (a) requires routine division of complex numbers and finding modulus. Part (b) involves using the argument condition to set up and solve an equation, which is a common textbook exercise. While it requires algebraic manipulation, the techniques are well-practiced and the question structure is typical for this topic. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
$$z = \frac{a + 3i}{2 + ai}, \quad a \in \mathbb{R}.$$
\begin{enumerate}[label=(\alph*)]
\item Given that $a = 4$, find $|z|$. [3]
\item Show that there is only one value of $a$ for which $\arg z = \frac{\pi}{4}$, and find this value. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q13 [9]}}