Do arithmetic on complex numbers: addition, subtraction, multiplication, division, plus magnitude and conjugate.
Enter two complex numbers and pick an operation.
Enter numbers to see the result.
Addition and subtraction work part by part: real with real, imaginary with imaginary. Multiplication uses the FOIL-style rule (ac - bd) + (ad + bc)i, remembering that i squared is -1. Division multiplies top and bottom by the conjugate of the divisor to clear i from the denominator.
The magnitude |z| = sqrt(x^2 + y^2) is the distance from the origin in the complex plane. The conjugate flips the sign of the imaginary part, and a number times its conjugate always gives a real number: the squared magnitude.