More Notation and Terminology

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.
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The Complex Plane