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how can i do this, applying Rouche Theorem and Cauchy Argument Principle?

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- Dec 3rd 2007, 10:03 PMhanahoucomplex analysis: integrals
http://i3.photobucket.com/albums/y57...ty/prob3-1.jpg

how can i do this, applying Rouche Theorem and Cauchy Argument Principle? - Dec 4th 2007, 08:38 AMThePerfectHacker
Use Cauchy's Argument Principle.

1) where is the number of poles and is the number of zeros (both counting multiplicity). Thus, this equation tells us that but because ia analytic on . Thus, the function has two zeros and within the unit disk (and I let so if it is the same zero of multiplicity two).

2) . Thus, .

3) .

Now solve for .