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what is the cauchy-coursat theorem state specifically in word? Is it calculate the area or the legth,which area and what legth? please give a example! And what is deformation of contour?

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    Deformation of contour refers to homotopy. This whole machinery is dealt with nicely in John Conway's complex analysis book.2011-07-10

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http://en.wikipedia.org/wiki/Cauchy-Goursat_theorem

Contour integrals in the complex plane can't be interpreted in terms of length or area.

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    But why is it represent as number?2011-07-10