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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

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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.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)FP2Complex NumbersDe Moivre theorem-
AQA A2 Further Maths 2017Pure MathsFurther Complex NumbersDe Moivre Theorem-
AQA AS/A2 Further Maths 2017Pure MathsFurther Complex NumbersDe Moivre Theorem-
CCEA A-Level (NI)FP2Complex NumbersDe Moivre theorem-
CIE A-Level (UK)P3Complex NumbersDe Moivre theorem-
Edexcel A-Level (UK - Pre-2017)FP2Complex NumbersDe Moivre theorem-
Edexcel A2 Further Maths 2017Core Pure MathsComplex NumbersDe Moivre Theorem-
Edexcel AS/A2 Further Maths 2017Core Pure MathsComplex NumbersDe Moivre Theorem-
I.B. Higher Level1Complex NumbersDe Moivre theorem-
Methods (UK)M3Complex NumbersDe Moivre theorem-
OCR A-Level (UK - Pre-2017)FP3Complex NumbersDe Moivre theorem-
OCR A2 Further Maths 2017Pure CoreFurther Complex NumbersDe Moivre Theorem-
OCR MEI A2 Further Maths 2017Core Pure BComplex NumbersDe Moivre Theorem-
OCR-MEI A-Level (UK - Pre-2017)FP2Complex NumbersDe Moivre theorem-
Scottish Advanced HighersM2Complex NumbersDe Moivre theorem-
Scottish (Highers + Advanced)AM2Complex NumbersDe Moivre theorem-
Universal (all site questions)CComplex NumbersDe Moivre theorem-
WJEC A-Level (Wales)FP2Complex NumbersDe Moivre theorem-