| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Direct nth roots: general complex RHS |
| Difficulty | Standard +0.3 This is a standard Further Maths FP2 question testing routine application of modulus-argument form and de Moivre's theorem. Part (a) requires straightforward calculation of r and θ, part (b) is direct application of de Moivre's theorem to cube a complex number, and part (c) involves finding fourth roots using the standard formula with k=0,1,2,3. While it's Further Maths content (inherently harder), the question follows a completely standard template with no problem-solving or novel insight required, making it slightly easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02q De Moivre's theorem: multiple angle formulae4.02r nth roots: of complex numbers |
$z = -8 + (8\sqrt{3})i$
\begin{enumerate}[label=(\alph*)]
\item Find the modulus of $z$ and the argument of $z$. [3]
\end{enumerate}
Using de Moivre's theorem,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find $z^3$. [2]
\item find the values of $w$ such that $w^4 = z$, giving your answers in the form $a + ib$, where $a, b \in \mathbb{R}$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q4 [10]}}