What is "complex conjugate"

n. (context mathematics English) Of a complex number ''x'', the complex number $overline\; x$ formed by changing the sign of the imaginary part: ''The complex conjugate of'' a + bi ''is'' a - bi.

In mathematics, the complex conjugate of a complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of 3 + 4i is 3 − 4i.

In polar form, the conjugate of ρe is ρe. This can be shown using Euler's formula.

Complex conjugates are important for finding roots of polynomials. According to the complex conjugate root theorem, if a complex number is a root to a polynomial in one variable with real coefficients (such as the quadratic equation or the cubic equation), so is its conjugate.