Complex conjugation

From Knowino
Jump to: navigation, search

In mathematics, complex conjugation is an operation on complex numbers which reverses the sign of the imaginary part, that is, it sends z = x + iy to the complex conjugate \bar z = x-iy.

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: \overline{z+w} = \bar z + \bar w and \overline{zw} = \bar z \bar w. 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.

Information.svg Some content on this page may previously have appeared on Citizendium.
Personal tools