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.
Formula
Conjugate of a + bi is a − bi; z · z̄ = a² + b² = |z|²
- The conjugate flips the sign of the imaginary part.
- Multiplying a complex number by its conjugate gives a real number equal to the modulus squared.
3 + 4i
Inputs
- Real part (a): 3
- Imaginary part (b): 4
Conjugate is 3 − 4i; modulus 5; z·z̄ = 25.
Frequently asked questions
What is a complex conjugate?
The complex number with the same real part but the opposite sign on the imaginary part: the conjugate of a + bi is a − bi.