| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Modulus-argument form conversion |
| Difficulty | Moderate -0.3 Part (a) is straightforward application of arctan with quadrant adjustment. Part (b) requires rationalizing a complex denominator and using the modulus formula to find A, which is standard FP1 technique. Part (c) uses the argument property arg(w/z) = arg(w) - arg(z). All parts are routine Further Maths exercises with no novel problem-solving required, making this 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 forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02f Convert between forms: cartesian and modulus-argument |
$$z = -4 + 6i.$$
\begin{enumerate}[label=(\alph*)]
\item Calculate $\arg z$, giving your answer in radians to 3 decimal places. [2]
\end{enumerate}
The complex number $w$ is given by $w = \frac{A}{2 - i}$, where $A$ is a positive constant. Given that $|w| = \sqrt{20}$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find $w$ in the form $a + ib$, where $a$ and $b$ are constants, [4]
\item calculate $\arg \frac{w}{z}$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q24 [9]}}