It's already been mentioned that the rectilinear coordinates of a complex
number in the complex plane are called the real part and
imaginary part, respectively.

We also have special notation and various names for the polar
coordinates
of a complex number :

The complex conjugate of is denoted
(or ) and is defined by

where, of course,
.

In general, you can always obtain the complex conjugate of any expression
by simply replacing with . In the complex plane, this is a vertical flip about the real axis; i.e., complex conjugation
replaces each point in the complex plane by its mirror image on the
other side of the axis.