Working with complex numbers
A complex number has the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (√-1). Addition and subtraction combine the real and imaginary parts separately, multiplication uses (a+bi)(c+di) = (ac-bd) + (ad+bc)i, and division multiplies by the conjugate of the denominator to clear the imaginary part from below the fraction line.
How to use this calculator
Enter the real and imaginary parts of both complex numbers (z1 = a + bi and z2 = c + di), choose an operation, and the calculator returns the real part, imaginary part, and modulus (distance from the origin) of the result.
Dividing by zero (a complex number with both parts equal to zero) is undefined, so the calculator returns a result of 0 in that case. This tool is for general math and educational use.