| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Direct nth roots: general complex RHS |
| Difficulty | Standard +0.3 This is a standard FP2 question on finding nth roots of complex numbers. Students must convert to modulus-argument form, apply De Moivre's theorem to find all four roots, and plot them. While it requires multiple steps (finding r and θ, dividing argument by 4, adding 2πk/4 for k=0,1,2,3), this is a routine textbook exercise with well-practiced techniques. The Argand diagram part is straightforward once roots are found. Slightly easier than average A-level due to its mechanical nature. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02q De Moivre's theorem: multiple angle formulae4.02r nth roots: of complex numbers |
3. (a) Find the four roots of the equation $z ^ { 4 } = 8 ( \sqrt { 3 } + \mathrm { i } )$ in the form $z = r \mathrm { e } ^ { \mathrm { i } \theta }$\\
(b) Show these roots on an Argand diagram.\\
\begin{center}
\end{center}
\hfill \mbox{\textit{Edexcel FP2 2016 Q3 [7]}}