The Argument Principle in Complex Analysis

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Let be a closed contour parameterized by
in the range
, and
a function meromorphic inside and on
. Define
for some
. The argument principle relates the change in argument of
as
describes
once in the positive direction to the number of zeros and poles inside the contour. The change in argument for one complete circuit around
is given by
. The Argument Principle then states:
, where
and
are the number of zeros and poles inside the contour, counting multiplicities.
Contributed by: Dominic Milioto (March 2011)
Open content licensed under CC BY-NC-SA
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