Math Calculators

Complex Conjugate Calculator

Find the complex conjugate and modulus (absolute value) of a complex number a + bi.

Conjugate real part —

Conjugate imaginary part —

Modulus |a + bi| —

About the Complex Conjugate Calculator

The complex conjugate of a + bi is a − bi — the same real part, with the sign of the imaginary part flipped. Multiplying a complex number by its conjugate always produces a real number, which is why conjugates are used to simplify division of complex numbers.

Formula: Conjugate of (a + bi) = a − bi · Modulus = √(a² + b²)

The modulus represents the distance of the point (a, b) from the origin on the complex plane, and is unaffected by conjugation.