| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Direct nth roots: general complex RHS |
| Difficulty | Moderate -0.3 This is a standard Further Maths FP2 question testing routine conversion to modulus-argument form and De Moivre's theorem for cube roots. Part (a) requires straightforward calculation of r and θ, while part (b) applies the standard formula for nth roots with no novel insight needed. The arithmetic is slightly more involved than basic C3 complex numbers, but this is a textbook exercise that any well-prepared FP2 student should handle comfortably. |
| Spec | 4.02b Express complex numbers: cartesian and modulus-argument forms4.02f Convert between forms: cartesian and modulus-argument4.02q De Moivre's theorem: multiple angle formulae |
\begin{enumerate}[label=(\alph*)]
\item Express the complex number $-2 + (2\sqrt{3})i$ in the form $r(\cos \theta + i \sin \theta)$, $-\pi < \theta \leq \pi$ [3]
\item Solve the equation
$$z^3 = -2 + (2\sqrt{3})i$$
giving the roots in the form $r(\cos \theta + i \sin \theta)$, $-\pi < \theta \leq \pi$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q3 [8]}}