# 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.

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Contributed by: Dominic Milioto (March 2011)

Open content licensed under CC BY-NC-SA

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