Difference between revisions of "Imaginary part"
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Latest revision as of 15:56, 5 September 2008
Any complex number can be written in the form
where
is the imaginary unit and
and
are real numbers. Then the imaginary part of
, usually denoted
or
, is just the value
. Note in particular that the imaginary part of every complex number is real.
Geometrically, if a complex number is plotted in the complex plane, its imaginary part is its -coordinate (ordinate).
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
.