| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus modulus/argument |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing standard complex number operations: modulus (direct application of formula), argument (arctan with quadrant adjustment), division (multiply by conjugate), and basic algebraic manipulation. While it's Further Maths content, all parts are routine applications of techniques with no problem-solving insight required, making it slightly easier than an average A-level question overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02c 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 |
\begin{enumerate}
\item The complex number $z$ is given by
\end{enumerate}
$$z = - 7 + 3 i$$
Find\\
(a) $| z |$\\
(b) $\arg z$, giving your answer in radians to 2 decimal places.
Given that $\frac { z } { 1 + \mathrm { i } } + w = 3 - 6 \mathrm { i }$\\
(c) find the complex number $w$, giving your answer in the form $a + b \mathrm { i }$, where $a$ and $b$ are real numbers. You must show all your working.\\
(d) Show the points representing $z$ and $w$ on a single Argand diagram.\\
\hfill \mbox{\textit{Edexcel F1 2017 Q5 [8]}}