| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus modulus/argument |
| Difficulty | Moderate -0.8 This is a routine Further Maths question testing basic complex number operations: plotting on Argand diagram, finding modulus, division by multiplying by conjugate, and finding argument. All techniques are standard with no problem-solving required, though it's slightly more involved than single-step recall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z)4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
The complex numbers $z_1$ and $z_2$ are given by
$$z_1 = 3 + 5\text{i} \quad \text{and} \quad z_2 = -2 + 6\text{i}$$
\begin{enumerate}[label=(\alph*)]
\item Show $z_1$ and $z_2$ on a single Argand diagram.
[2]
\item Without using your calculator and showing all stages of your working,
\begin{enumerate}[label=(\roman*)]
\item determine the value of $|z_1|$
[1]
\item express $\frac{z_1}{z_2}$ in the form $a + b\text{i}$, where $a$ and $b$ are fully simplified fractions.
[3]
\end{enumerate}
\item Hence determine the value of $\arg \frac{z_1}{z_2}$
Give your answer in radians to 2 decimal places.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2022 Q2 [8]}}