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- Lef f be a function which is analytic inside...
- Write and equation...
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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 ...
Analytic Funcitons and Contours are investigated.