In the geometrical interpretation in terms of the Argand diagram, complex conjugation is represented by reflection in the x-axis. The complex numbers left fixed by conjugation are precisely the real numbers.
Conjugation respects the algebraic operations of the complex numbers: and . Hence conjugation represents an automorphism of the field of complex numbers over the field of real numbers, and is the only non-trivial automorphism. One can say it is impossible to tell which is i and which is -i.