Argument principle | Wikipedia Easy Search

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The simple contour C (black), the zeros of f (blue) and the poles of f (red). Here we have ${\frac {1}{2\pi i}}\oint _{C}{f'(z) \over f(z)}\,dz=4-5.\,$

In complex analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.

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