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.