Real part
Any complex number can be written in the form
where
is the imaginary unit and
and
are real numbers. Then the real part of
, usually denoted
or
, is just the value
.
Geometrically, if a complex number is plotted in the complex plane, its real part is its -coordinate (ordinate).
A complex number is real exactly if
.
The function can also be defined in terms of the complex conjugate
of
:
. (Recall that if
,
).
Examples
. Note in particular that
is not in general a multiplicative function,
for arbitrary complex numbers
.
Practice Problem 1
Find the conditions on and
so that
.