About the Complex Conjugate Calculator
Find the complex conjugate of a + bi, and the product z·z̄ (always a real number equal to |z|²).
Also known as: conjugate of complex number, z bar, complex conjugate.
How to use this calculator
- Enter z.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
conj(a + bi) = a − bi
Worked example
Using the values pre-filled in the calculator above:
- z: 5 - 3i
the calculator returns:
- Conjugate z̄: 5 + 3i
- z · z̄: 34