Quote:
Originally Posted by durham2  Having trouble solving this contour integral. Evaluate the integral e^5z/z^5 where c is the circle |z|=1 traversed in clockwise direction? Any suggestions where to start? | Note that  is a pole of order 5. We can apply the residue theorem to this by noting that ![\text{Res}\left(f,0\right)=\frac{1}{4!}\lim_{z\to 0}\frac{\,d^4}{\,dz^4}\left[z^5f\!\left(z\right)\right]=\frac{1}{4!}\lim_{z\to 0}\frac{\,d^4}{\,dz^4}e^{5z}=\frac{1}{4!}\lim_{z\to0}5^4e^{5z}=\frac{625}{24}](http://www.mathhelpforum.com/math-help/latex2/img/b7877ed12dadfdf9c4db724bdb01f127-1.gif "\text{Res}\left(f,0\right)=\frac{1}{4!}\lim_{z\to 0}\frac{\,d^4}{\,dz^4}\left[z^5f\!\left(z\right)\right]=\frac{1}{4!}\lim_{z\to 0}\frac{\,d^4}{\,dz^4}e^{5z}=\frac{1}{4!}\lim_{z\to0}5^4e^{5z}=\frac{625}{24}")
Thus, 
Since we're moving clockwise, it follows that the result will be negative.
Does this make sense?
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contour integral-need help 
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