Add, subtract, multiply, or divide complex numbers with a clean live result panel.
Last updated: June 2026 | By Patchworkr Team
Operation
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.
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.
Addition / Subtraction
(a + bi) ± (c + di) = (a ± c) + (b ± d)i
Multiplication / Division
Uses the standard distributive rule and division by the conjugate denominator.
Related Tools