# Complex Variables : Analytic Funcitons and Contours

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Please see the attached file for the fully formatted problems.

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- Lef f be a function which is analytic inside...

- Write and equation...

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(See attached file for full problem description)

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#### Solution Preview

Hello there

Regarding file 80-2, if we pick any point on the curve Gamma, and move that point along the curve once so that it comes back to its original position, we see the tangent moves smoothly through 3 revolutions, so the change in Arg f(z) is 6 Pi radians.

By the argument principle that the change in arg f = 2 Pi * (Z-P), we see

Z - P = 3. As f is analytic inside C, it has no poles there, so Z, the no. of zeros, is 3 inside f.

(Incidentally, the argument principle follows from the result that ...

#### Solution Summary

Analytic Funcitons and Contours are investigated.

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