| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Parameter from real/imaginary condition |
| Difficulty | Moderate -0.3 This is a straightforward Further Pure 1 complex number question requiring standard techniques: multiply by conjugate to find real/imaginary parts, solve a simple quadratic, then find argument using arctan. While it's FP1 content, the algebraic manipulation is routine and the question follows a predictable template with clear signposting. |
| 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 |
The complex number $z$ is defined by
$$z = \frac{a + 2i}{a - 1}, \quad a \in \mathbb{R}, a > 0 .$$
Given that the real part of $z$ is $\frac{1}{2}$ , find
\begin{enumerate}[label=(\alph*)]
\item the value of $a$, [4]
\item the argument of $z$, giving your answer in radians to 2 decimal places. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q46 [7]}}