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.
Next Section: Elementary RelationshipsPrevious Section: The Complex Plane