| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Parameter from argument condition |
| Difficulty | Standard +0.8 This is a Further Maths question requiring algebraic manipulation of complex fractions, expressing in Cartesian form with parameters, then using the argument condition to solve a quadratic. It combines multiple techniques (complex division, equating real/imaginary parts, argument formula) but follows a clear structured path without requiring deep insight. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms |
\begin{enumerate}
\item Given that
\end{enumerate}
$$\frac { 3 z - 1 } { 2 } = \frac { \lambda + 5 i } { \lambda - 4 i }$$
where $\lambda$ is a real constant,\\
(a) determine $z$, giving your answer in the form $x + y i$, where $x$ and $y$ are real and in terms of $\lambda$.
Given also that $\arg z = \frac { \pi } { 4 }$\\
(b) find the possible values of $\lambda$.
\hfill \mbox{\textit{Edexcel F1 2024 Q9 [6]}}