| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Direct nth roots: find and express roots |
| Difficulty | Standard +0.8 This is a Further Pure question requiring conversion to polar form, application of de Moivre's theorem for roots, and careful angle arithmetic to find three distinct cube roots. While the technique is standard for FP3, it requires multiple steps (finding modulus, argument, applying root formula, finding all three roots) and precision with angles, making it moderately challenging but still a routine application of complex number theory. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02r nth roots: of complex numbers |
Find the cube roots of $\frac{1}{2}\sqrt{3} + \frac{1}{2}i$, giving your answers in the form $\cos \theta + i \sin \theta$, where $0 \leqslant \theta < 2\pi$. [4]
\hfill \mbox{\textit{OCR FP3 Q1 [4]}}