conjugate (of a complex number) For any complex number z, where z = x + yi, its conjugate (also denoted z) is equal to x−yi. As a point in the complex plane represents the mirror image of z in the real axis. The complex conjugate satisfies,

and so complex conjugation is a field automorphism of ℂ. Other identities include 
It is an important fact that if the complex number α is a root of a polynomial equation 
where a1,…, an are real, then is also a root of this equation. |