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Complex Number Calculator

Add, subtract, multiply and divide complex numbers of the form a + bi, with the modulus and argument shown alongside.

Complex number calculator

Result: —
Modulus: — · Argument: —
z1 = a + bi and z2 = c + di. The argument is measured in degrees.

How to use the Complex Number Calculator

  1. Pick the operation you want: add, subtract, multiply or divide.
  2. Enter the real and imaginary parts of z1 and z2.
  3. Read the result together with its modulus and argument.

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Frequently Asked Questions

Common questions about the free online complex number calculator.

A complex number has a real part and an imaginary part, written as a + bi, where i is the square root of minus one.
Add the real parts together and add the imaginary parts together. For example (3 + 2i) plus (1 + 4i) gives 4 + 6i.
Multiply the terms like binomials and replace i squared with minus one. The tool does this automatically and simplifies the result.
Multiply the top and bottom by the conjugate of the divisor, then simplify. The calculator performs that step for you.
The modulus is the distance from the origin, and the argument is the angle from the positive real axis, shown here in degrees.
Yes. When the imaginary parts cancel out, the answer is a plain real number and the tool shows it without an i term.
Yes. Negative real parts, negative imaginary parts and decimals are all accepted in both complex numbers.
Dividing by zero is undefined in complex arithmetic, so the tool reports an error instead of returning a meaningless value.
No. Every calculation happens locally in your browser and nothing you type is ever transmitted or stored.

Last updated: October 10, 2026