The equation z^n=a+ib \quad has n roots. We can use De Moivre's theorem to find them.
De Moivre's Theorem: (\cos \theta + i \sin \theta)^n = \cos n\theta + i \sin n\theta
De Moivre's Theorem: (\cos \theta + i \sin \theta)^n = \cos n\theta + i \sin n\theta
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Glossary
equation
A statement that two mathematical expressions are equal.
union
The union of two sets A and B is the set containing all the elements of A and B.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AQA A-Level (UK - Pre-2017) | FP2 | Complex Numbers | De Moivre theorem | - |
| AQA A2 Further Maths 2017 | Pure Maths | Further Complex Numbers | De Moivre Theorem | - |
| AQA AS/A2 Further Maths 2017 | Pure Maths | Further Complex Numbers | De Moivre Theorem | - |
| CCEA A-Level (NI) | FP2 | Complex Numbers | De Moivre theorem | - |
| CIE A-Level (UK) | P3 | Complex Numbers | De Moivre theorem | - |
| Edexcel A-Level (UK - Pre-2017) | FP2 | Complex Numbers | De Moivre theorem | - |
| Edexcel A2 Further Maths 2017 | Core Pure Maths | Complex Numbers | De Moivre Theorem | - |
| Edexcel AS/A2 Further Maths 2017 | Core Pure Maths | Complex Numbers | De Moivre Theorem | - |
| I.B. Higher Level | 1 | Complex Numbers | De Moivre theorem | - |
| Methods (UK) | M3 | Complex Numbers | De Moivre theorem | - |
| OCR A-Level (UK - Pre-2017) | FP3 | Complex Numbers | De Moivre theorem | - |
| OCR A2 Further Maths 2017 | Pure Core | Further Complex Numbers | De Moivre Theorem | - |
| OCR MEI A2 Further Maths 2017 | Core Pure B | Complex Numbers | De Moivre Theorem | - |
| OCR-MEI A-Level (UK - Pre-2017) | FP2 | Complex Numbers | De Moivre theorem | - |
| Scottish Advanced Highers | M2 | Complex Numbers | De Moivre theorem | - |
| Scottish (Highers + Advanced) | AM2 | Complex Numbers | De Moivre theorem | - |
| Universal (all site questions) | C | Complex Numbers | De Moivre theorem | - |
| WJEC A-Level (Wales) | FP2 | Complex Numbers | De Moivre theorem | - |