Complex Number Operations Calculator
Add, subtract, multiply and divide two complex numbers.
Reviewed by the Calculation Machine team · How we check our maths
Your values
ⓘ Live results
Results
- Sum
- 4 - 2i
- Difference
- 2 + 6i
- Product
- 11 - 10i
- Quotient
- -0.2941 + 0.8235i
Quick answer
Complex numbers combine like binomials, remembering that i^2 = -1, and division multiplies by the conjugate.
The formula
(a+bi)(c+di) = (ac-bd)+(ad+bc)i
Worked example
Worked example
Using the values the calculator loads with.
Inputs
- Real part of z13
- Imaginary part of z12
- Real part of z21
- Imaginary part of z2-4
Result
- Sum4 - 2i
- Difference2 + 6i
- Product11 - 10i
- Quotient-0.2941 + 0.8235i
How to use the Complex Number Operations Calculator
- 1Enter the real and imaginary parts of both complex numbers.
- 2Sum, difference and product follow standard binomial expansion with i^2=-1.
- 3Division multiplies numerator and denominator by the conjugate of z2.
Frequently asked questions
What is i^2?
By definition, i^2 = -1.
What if z2 is zero?
Division is undefined when the denominator complex number is 0+0i.
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Report an error