| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Modulus and argument calculations |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic complex number operations: finding modulus and argument of a complex number in Cartesian form, converting from polar form, and applying quotient rules. All parts are direct applications of standard formulas with no problem-solving required, making it easier than average even for Further Maths students. |
| 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, divide |
$z = 5\sqrt{3} - 5i$
Find
\begin{enumerate}[label=(\alph*)]
\item $|z|$, [1]
\item $\arg(z)$, in terms of $\pi$. [2]
\end{enumerate}
$$w = 2\left[\cos \frac{\pi}{4} + i\sin \frac{\pi}{4}\right]$$
Find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item $\left|\frac{w}{z}\right|$, [1]
\item $\arg\left(\frac{w}{z}\right)$, in terms of $\pi$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q2 [6]}}