MATH
Complex Number Arithmetic Calculator
Add, multiply or divide two complex numbers and show both result components.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Complex Number Arithmetic Calculator
Enter Cartesian real and imaginary components. Select one operation and read the real and imaginary components together as the resulting complex number.
The calculation
(a+bi)(c+di) = (ac−bd) + (ad+bc)i; division uses the conjugate
Worked example
(1+2i) × (3+4i) gives −5+10i; the primary result displays its real component.
Assumptions and limits
Does not parse symbolic expressions or perform polar arithmetic. Division by a zero complex number is rejected.
Common questions
Which inputs should I use?
Enter Cartesian real and imaginary components. Select one operation and read the real and imaginary components together as the resulting complex number.
What does the result exclude?
Does not parse symbolic expressions or perform polar arithmetic. Division by a zero complex number is rejected.