Residue Calculus: Evaluating Poles and Contours

[eeuler]

Homework Statement

The Attempt at a Solution

So there are poles at: z=$$\pm2$$ and at z= -1 of order 4. Right?

My query is, when evaluating these poles (using the residue theorem), is it right that for (i) Z = 1/2, no residues lie in that contour?
for (iii), do all residues lie in the contour?

 

[Dick]

Right about the poles, but for the rest, are you just guessing? Why don't you draw a graph? No, I don't think the triangle in iii) includes all poles.

 

[eeuler]

^^I wasn't sure how to determine whether a pole is inside a specified contour but my tutor suggested drawing a graph, which i have been doing, in which case shouldn't (i) have no poles in the contour? As for (iii) then, would Z=+2, and Z=-1 lie in the contour?

 

[Dick]

Your tutor is wise. Yes, i) contains no poles and iii) contains z=(-1) and z=2.

 

[eeuler]

^^Thanks :)