Complex Number Calculator

Complex Number Calculator

Add, subtract, multiply, or divide complex numbers with a clean live result panel.

Last updated: June 2026 | By Patchworkr Team

Complex Arithmetic

Operation

Operation
3 + 2i + 1 + 4i
Result
4 + 6i
Complex arithmetic follows the standard rules for adding, subtracting, multiplying, and dividing numbers of the form a + bi.

What is a Complex Number?

A complex number has a real part and an imaginary part. It is written as a + bi, where i is the imaginary unit and i² = -1.

How to Use It

  1. Enter the real and imaginary parts of both numbers.
  2. Choose an operation.
  3. Read the expression and the computed result on the right.

What happens when the denominator is zero?

Division is rejected if the second complex number is exactly 0 + 0i.

Does the calculator accept decimals?

Yes. Both parts accept finite decimals and scientific notation.

Why show the operation separately?

It makes it easier to verify the exact formula used for the calculation.

What if I enter invalid text?

Invalid input is rejected instead of being silently converted to zero.

Formula Check

Addition / Subtraction

(a + bi) ± (c + di) = (a ± c) + (b ± d)i

Multiplication / Division

Uses the standard distributive rule and division by the conjugate denominator.

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