| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2009 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Direct nth roots: find and express roots |
| Difficulty | Standard +0.3 This is a standard Further Maths FP3 question requiring conversion to polar form, application of De Moivre's theorem for nth roots, and expressing three roots in trigonometric form. While it involves multiple steps (finding modulus/argument, dividing argument by 3, adding 2π/3 for each root), these are routine procedures for Further Maths students with no novel problem-solving required. Slightly easier than average A-level difficulty overall due to its procedural nature. |
| Spec | 4.02r nth roots: of complex numbers |
1 Find the cube roots of $\frac { 1 } { 2 } \sqrt { 3 } + \frac { 1 } { 2 } \mathrm { i }$, giving your answers in the form $\cos \theta + \mathrm { i } \sin \theta$, where $0 \leqslant \theta < 2 \pi$.
\hfill \mbox{\textit{OCR FP3 2009 Q1 [4]}}