| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Modulus-argument form conversion |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring standard complex number operations: computing z², multiplying complex numbers, finding modulus and argument, and basic Argand diagram work. While it involves multiple steps and is from FP1 (inherently harder material), the techniques are routine applications of formulas with no problem-solving insight required. The angle calculation follows directly from argument properties. |
| 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, divide4.02k Argand diagrams: geometric interpretation |
Given that $z = 2 - 2i$ and $w = -\sqrt{3} + i$,
\begin{enumerate}[label=(\alph*)]
\item find the modulus and argument of $wz^2$. [6]
\item Show on an Argand diagram the points $A$, $B$ and $C$ which represent $z$, $w$ and $wz^2$ respectively, and determine the size of angle $BOC$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q15 [10]}}