Integrate the funtion around 4 different contours

g(z)=z^2+1/z^2-1

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- Oct 27th 2009, 12:10 PMbookie88complex integration
Integrate the funtion around 4 different contours

g(z)=z^2+1/z^2-1 - Oct 27th 2009, 12:49 PMtonio
- Oct 28th 2009, 02:26 AMwalleye
the significance of different contours lies in whether or not your contour encircles (if its a closed contour) the singular points of g(z)

singular points are just where g(z) is undefined, so here, where the denomenator equals 0

where z=1 or -1

so a contour that doesnt encircle these points, would be

$\displaystyle \gamma = 3+e^{i\theta}$

integrating g(z) around this contour gives 0

this is by the residue theorem, closed contour integration theorem... something along those lines

for a contour that encircles the singularities

e.g.

$\displaystyle \gamma = 2e^{i\theta}$

you have to calculate the residues of g(z) at the points of singularities - Oct 28th 2009, 03:36 AMmr fantastic
We all understand what you're saying. However, the question does not specify which four contours to use so the question is answered by choosing any four contours at all, including the four suggested in post #2 .... (A flaw in either the original question or in how the question has been posted ....)