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Complex Number Calculators

Complex Multiplication Calculator

Multiply two complex numbers using FOIL and i² = −1, with the product in rectangular and polar form.

Enter values

Results update as you type.

Result

z₁ × z₂

11 − 2i

Polar form
11.18033989 ∠ -10.304846°
Modulus |z|
11.18033989

About the Complex Multiplication Calculator

Multiply two complex numbers using FOIL and i² = −1, with the product in rectangular and polar form.

Also known as: multiply complex numbers, product of complex numbers.

How to use this calculator

  1. Enter z₁, z₂.
  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

(a + bi)(c + di) = (ac − bd) + (ad + bc)i

Worked example

Using the values pre-filled in the calculator above:

  • z₁: 3 + 4i
  • z₂: 1 - 2i

the calculator returns:

  • z₁ × z₂: 11 − 2i
  • Polar form: 11.18033989 ∠ -10.304846°
  • Modulus |z|: 11.18033989