Complex Number Calculator
Add, subtract, multiply, or divide two complex numbers.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter two complex numbers and an operation to compute the result.
Your result
4 + 6i
Result
Real part4
Imaginary part6
AI explanation
Formula
Add/subtract: combine parts directly. Multiply: (a+bi)(c+di) = (ac−bd) + (ad+bc)i. Divide: multiply by the conjugate.Worked example
(3+4i) x (1+2i)
| Field | Value |
|---|---|
| Real part 1 | 3 |
| Imaginary part 1 | 4 |
| Real part 2 | 1 |
| Imaginary part 2 | 2 |
| Operation | multiply |
| Real part | -5 |
| Imaginary part | 10 |
| Result | -5 + 10i |
Assumptions
- Enter each complex number as its real and imaginary parts separately (e.g. 3 + 4i is real=3, imag=4).
Frequently asked questions
How do you multiply complex numbers?
(a+bi)(c+di) = ac + adi + bci + bdi² = (ac − bd) + (ad + bc)i, using i² = −1.
How do you divide complex numbers?
Multiply both the numerator and denominator by the denominator's complex conjugate, which makes the denominator a real number.
I need to convert to polar form (magnitude and angle) — is there a calculator for that?
Yes — see the Complex Number Polar Form Calculator.