Complex Variables - solutions to 11/9/09 integration problems
1) -e2-1. I recommend the antiderivative theorem, using the antiderivative ez, which is a valid antiderivative everywhere.
2) Same as #1, again by the same antiderivative theorem.
3) 6![[pi]](../../graphics/symbols/pi.gif)
i. Parametrization is easy here; z(t) = i + 4eit, t![[belongs to]](../../graphics/symbols/elmt_of.gif)
[0,2], almost the entire problem cancels away.
4) Zero, by the Cauchy-Goursat theorem: Draw a sketch of the contour, and locate f's only singularity to see why the theorem applies.
5) -4+2i. The antiderivative theorem works nicely.
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