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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 You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

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:

SyllabusModuleSectionTopic
Core PureComplex NumbersDe Moivre Theorem
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