Formula and method
For multiplication, (a + bi)(c + di) = (ac − bd) + (ad + bc)i. Division multiplies by the divisor’s complex conjugate.
Worked example
(3 + 2i)(1 − 4i) = 11 − 10i. The magnitude is √221, approximately 14.8661.
Complex Number Calculator
Add, subtract, multiply or divide complex numbers and inspect the result’s magnitude and principal argument.
Printed from Calxy · https://www.calxy.net/math/complex-number-calculator
Complex result11 − 10i
-1000000000 – 1000000000
-1000000000 – 1000000000
-1000000000 – 1000000000
-1000000000 – 1000000000
Complex result
11 − 10i
- Magnitude14.8661
- Argument-42.2737 degrees
Rectangular complex arithmetic with real-number floating-point calculations. Argument is the principal angle in degrees; zero has no defined argument.
How this was calculated
(a + bi)(c + di) = (ac − bd) + (ad + bc)i.
Frequently asked questions
What is the argument of zero?
It is undefined because zero has no direction in the complex plane. The calculator labels it explicitly instead of giving a misleading angle.
Last updated . Results are estimates for informational purposes only.