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 Exercise [07.01] b 
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Joined: 07 Jun 2008, 08:21
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Post Exercise [07.01] b
Remember that z^n is a single-valued function of z, unlike \log z, which is multi-valued.

\int_a^bz^ndz=\frac{z^{n+1}}{n+1}\ |_a^b where a and b are any two points in the complex plane and n\ne-1

=\frac{b^{n+1}}{n+1}-\frac{a^{n+1}}{n+1}

For a closed loop a=b and because z^n is single-valued the integral vanishes and can be written as

\oint z^ndz=0\ n\ne-1


13 Jul 2008, 22:17
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