| Exam Board | WJEC |
|---|---|
| Module | Further Unit 4 (Further Unit 4) |
| Year | 2024 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Direct nth roots: roots with geometric or algebraic follow-up |
| Difficulty | Standard +0.8 This is a Further Maths question requiring conversion to polar form, application of De Moivre's theorem for cube roots, and geometric calculation of triangle area from complex roots. While the techniques are standard for Further Maths (finding modulus/argument, dividing angles by 3, adding 2π/3 increments), it requires careful execution across multiple steps and the geometric insight that cube roots form an equilateral triangle. The area calculation adds computational complexity but follows from standard formulas. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02r nth roots: of complex numbers |
\begin{enumerate}[label=(\alph*)]
\item Express the three cube roots of $5 + 10\mathrm{i}$ in the form $re^{i\theta}$, where $0 \leq \theta < 2\pi$. [6]
\item The three cube roots of $5 + 10\mathrm{i}$ are plotted in an Argand diagram. The points are joined by straight lines to form a triangle. Find the area of this triangle, giving your answer correct to two significant figures. [5]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 4 2024 Q1 [11]}}