Math
Complex multiplication
Multiply two complex numbers entered as real and imaginary components.
Calculators / Math / Complex number division
Complex number division calculator
Divide two complex numbers entered as their real and imaginary components.
On this page
Quotient real part2.2
Quotient imaginary part-0.4
Calculator controls
How to calculate
Divide two complex numbers entered as their real and imaginary components.
Quotient real part =
(a*c+b*d)/(c^2+d^2)Quotient imaginary part =
(b*c-a*d)/(c^2+d^2)Worked example
- Numerator real part: 3
- Numerator imaginary part: 4
- Denominator real part: 1
- Denominator imaginary part: 2
- Quotient real part: 2.2
- Quotient imaginary part: -0.4
Assumptions and limits
The denominator must be nonzero. Read the result as its real component plus i times its imaginary component.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Divide two complex numbers entered as their real and imaginary components. Multiplying numerator and denominator by the conjugate removes the imaginary part from the denominator.
When this tool is useful
Multiplying numerator and denominator by the conjugate removes the imaginary part from the denominator.
Understanding your inputs
| Input | Example |
|---|---|
Numerator real part a | 3 |
Numerator imaginary part b | 4 |
Denominator real part c | 1 |
Denominator imaginary part d | 2 |
Frequently asked questions
Which assumptions matter for this result?
The denominator must be nonzero. Read the result as its real component plus i times its imaginary component.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.