The complex conjugate of a complex number is the number obtained by flipping the sign of its imaginary part.

The complex conjugate of a complex number z congruent a + b i is defined to be z^_ congruent a - b i. The conjugate matrix of a matrix A = (a_(i j)) is the matrix obtained by replacing each element a_(i j) with its complex conjugate, A^_ = (a^__(i j)). The complex conjugate is implemented in the Wolfram Language as Conjugate[z].

complex addition | complex analysis | complex division | complex exponentiation | complex modulus | complex multiplication | complex number | complex subtraction | conjugate matrix | conjugate transpose

Conjugate

high school level (California Algebra II standard)