For any complex number z, where z = x + yi, its conjugate $\overline{z}$ (also denoted z*) is equal to x−yi. As a point in the complex plane $\overline{z}$ 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,…, a_n are real, then $\overline{\alpha }$ is also a root of this equation.