| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Direct nth roots: general complex RHS |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring conversion to polar form, application of De Moivre's theorem for square roots, and careful angle arithmetic. While it involves multiple steps (finding modulus, argument, then two square roots), these are standard techniques with no conceptual difficulty beyond routine FP2 material. The 6 marks reflect mechanical work rather than problem-solving insight. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02q De Moivre's theorem: multiple angle formulae |
Solve the equation
$$z^2 = 4\sqrt{2} - 4\sqrt{2}i,$$
giving your answers in the form $r(\cos \theta + i \sin \theta)$, where $-\pi < \theta \leq \pi$. [6]
\hfill \mbox{\textit{Edexcel FP2 Q2 [6]}}