We also have special notation and various names for the radius and angle of a complex number expressed in polar coordinates :
The complex conjugate of is denoted and is defined by
where, of course, . Sometimes you’ll see the notation in place of , but we won’t use that here.
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; in other words, complex conjugation replaces each point in the complex plane by its mirror image on the other side of the axis.