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Complex Number Calculators

Complex Number Calculator

Add, subtract, multiply, divide and raise complex numbers to powers, with results in rectangular and polar form.

Enter values

Results update as you type.

Result

Result

11 − 2i

Polar form
11.18033989 ∠ -10.304846°
Modulus
11.18033989
Argument
-10.304846 °

About the Complex Number Calculator

Add, subtract, multiply, divide and raise complex numbers to powers, with results in rectangular and polar form.

Also known as: complex calculator, imaginary number calculator, a + bi calculator, complex arithmetic.

How to use this calculator

  1. Enter z₁, operation, z₂ (or n for power).
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

i² = −1 · z = a + bi = r(cos θ + i sin θ)

Worked example

Using the values pre-filled in the calculator above:

  • z₁: 3 + 4i
  • Operation: ×
  • z₂ (or n for power): 1 - 2i

the calculator returns:

  • Result: 11 − 2i
  • Polar form: 11.18033989 ∠ -10.304846°
  • Modulus: 11.18033989
  • Argument: -10.304846 °