| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Argument calculations and identities |
| Difficulty | Moderate -0.3 This is a straightforward FP1 complex numbers question requiring division by multiplying by conjugate (standard technique), then using the argument condition to solve for p. The steps are routine: divide complex numbers, simplify to a+ib form, apply tan(π/4)=1 to get b/a=1, solve linear equation. No novel insight needed, just methodical application of basic FP1 techniques. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
The complex numbers $z_1$ and $z_2$ are given by
$$z_1 = 5 + 3i,$$
$$z_1 = 1 + pi,$$
where $p$ is an integer.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{z_2}{z_1}$, in the form $a + ib$, where $a$ and $b$ are expressed in terms of $p$. [3]
\end{enumerate}
Given that $\arg \left( \frac{z_2}{z_1} \right) = \frac{\pi}{4}$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of $p$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q36 [5]}}