Difference between revisions of "Real part"
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Revision as of 07:00, 17 March 2008
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 (abscissa).
A complex number is real exactly when
.
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
.