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

## Software/Applets used on this page

## 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 |
---|---|---|---|

Core Pure | Complex Numbers | De Moivre Theorem | |

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 |