Go to content
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
Change
 Steps  
All
Change
 Steps  
All
O
O
O
O
    
+
r
-
    

Software/Applets used on this page

jsMath
This page uses jsMath
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:

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