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Complex Conjugate Calculator

a
b

Result

Conjugate3.000 - 4.000i
Modulus |z|5.0000
z · z̄ (= |z|²)25.000
↗ Math

Complex Conjugate Calculator The Complex Conjugate Calculator returns the conjugate of a complex number a + bi (which is a − bi), along with its modulus and the product z·z̄. Enter the real and imaginary parts. — free online calculator.

Formula

Conjugate of a + bi is a − bi; z · z̄ = a² + b² = |z|²
  • Complex Conjugate Calculator calculates its result from Bi, Conjugate Of A, Bi Is A. It uses the formula Conjugate of a + bi is a − bi; z · z̄ = a² + b² = |z|². Change any input to recalculate the result instantly.
  • The main inputs are Real part, Imaginary part. Enter them in the units and format shown in the calculator.
  • Keep comparable quantities in compatible units whenever the formula combines or compares them.
  • Changing any input above recalculates the result with the same calculation engine used by this page.

Example: Complex Conjugate

Inputs
  • Real part: 3
  • Imaginary part: 4 b

Using Bi = 2, Conjugate Of A = 3, Bi Is A = 4, the calculated result is 5.

Sample result: Calculating…

Frequently asked questions

What does the Complex Conjugate calculate?

Complex Conjugate Calculator The Complex Conjugate Calculator returns the conjugate of a complex number a + bi (which is a − bi), along with its modulus and the product z·z̄. Enter the real and imaginary parts. — free online calculator.

Which values should I enter?

Enter Real part, Imaginary part using the units and format shown beside each field.

What formula does this calculator use?

The calculator uses the following relationship: Conjugate of a + bi is a − bi; z · z̄ = a² + b² = |z|².

Why might my result differ from another source?

Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.

Does the result update automatically?

Yes. Changing an input updates the result using the same calculation engine shown on this page.

Page information

Updated: October 10, 2026