Complex Number Calculator
Add, subtract, multiply and divide complex numbers, and convert between rectangular (a + bi) and polar form (r∠θ), with modulus and conjugate.
How to use
- 1Enter the real and imaginary parts of each number.
- 2Choose the operation.
How it's calculated
(a + bi)(c + di) = (ac − bd) + (ad + bc)i. Division multiplies by the conjugate of the divisor. Modulus |z| = √(a² + b²); argument θ = atan2(b, a).
Frequently asked questions
What is i?
The imaginary unit, defined by i² = −1.
What is the complex conjugate?
The same number with the imaginary part's sign flipped: the conjugate of 3 + 4i is 3 − 4i.
Where are complex numbers used?
Electrical engineering (AC circuits), signal processing, quantum physics and control systems.