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To divide two complex numbers, multiply by the complex conjugate of the denominator.
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Summary/Background

graphic calculatorA note about graphic calculators
A graphic calculator, for example the TI-83 or similar model, can work with complex numbers.

complex number conversionscomplex number modeFirst select MODE and move down to select a+bi:
Then press 2nd QUIT and enter a complex number sum.

Software/Applets used on this page

jsMath
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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

complex number

A number of the form a+bi where i is the square root of -1, and a and b are real.

conjugate

of a complex number a+bi is a-bi.

denominator

the integer on the bottom of a fraction

mode

the value in a set of discrete data that occurs most frequently

union

The union of two sets A and B is the set containing all the elements of A and B.

work

Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AQA A-Level (UK - Pre-2017)FP2Complex NumbersComplex algebra
AQA AS Further Maths 2017Pure MathsComplex Number BasicsComplex Algebra
AQA AS/A2 Further Maths 2017Pure MathsComplex Number BasicsComplex Algebra
Core PureComplex NumbersComplex Algebra
CBSE XI (India)AlgebraComplex Numbers and Quadratic EquationsImaginary unit
CCEA A-Level (NI)FP1Complex NumbersComplex algebra
CIE A-Level (UK)P3Complex NumbersComplex algebra
Edexcel A-Level (UK - Pre-2017)FP1Complex NumbersComplex algebra
Edexcel AS Further Maths 2017Core Pure MathsComplex NumbersComplex Algebra
Edexcel AS/A2 Further Maths 2017Core Pure MathsComplex NumbersComplex Algebra
I.B. Higher Level1Complex NumbersComplex algebra
Methods (UK)M3Complex NumbersComplex algebra
OCR A-Level (UK - Pre-2017)FP1Complex NumbersComplex algebra
OCR AS Further Maths 2017Pure CoreComplex Number BasicsComplex Algebra
OCR MEI AS Further Maths 2017Core Pure AComplex Number BasicsComplex Algebra
OCR-MEI A-Level (UK - Pre-2017)FP1Complex NumbersComplex algebra
Pre-U A-Level (UK)7Complex NumbersComplex algebra
Scottish Advanced HighersM2Complex NumbersComplex algebra
Scottish (Highers + Advanced)AM2Complex NumbersComplex algebra
Universal (all site questions)CComplex NumbersComplex algebra
WJEC A-Level (Wales)FP1Complex NumbersComplex algebra