| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex arithmetic operations |
| Difficulty | Moderate -0.8 This is a routine Further Maths question testing standard complex number operations: division by multiplying by conjugate, finding modulus, and finding argument. While Further Maths content, these are mechanical procedures with no problem-solving required, making it easier than average overall but typical for introductory FP1 complex numbers. |
| 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, divide |
\begin{enumerate}
\item The complex numbers $z _ { 1 }$ and $z _ { 2 }$ are given by
\end{enumerate}
$$z _ { 1 } = 2 + 8 \mathrm { i } \quad \text { and } \quad z _ { 2 } = 1 - \mathrm { i }$$
Find, showing your working,\\
(a) $\frac { z _ { 1 } } { z _ { 2 } }$ in the form $a + b \mathrm { i }$, where $a$ and $b$ are real,\\
(b) the value of $\left| \frac { z _ { 1 } } { z _ { 2 } } \right|$,\\
(c) the value of $\arg \frac { z _ { 1 } } { z _ { 2 } }$, giving your answer in radians to 2 decimal places.\\
\hfill \mbox{\textit{Edexcel F1 Q1 [7]}}