Argument Principle - Interpretation of The Contour Integral

Interpretation of The Contour Integral

The contour integral can be interpreted in two ways:

  • as the total change in the argument of f(z) as z travels around C, explaining the name of the theorem; this follows from

and the relation between arguments and logarithms.

  • as 2πi times the winding number of the path foC around the origin, using the substitution w = f(z):

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