If then . So you are looking for fourth roots of –1. How do you find them? (Answer: De Moivre's theorem. Write –1 as and raise it to the power 1/4.)
I cant figure out where the singularities are on this Q!
Q: Use a large semicircular contour and the residue theorem to evaluate:
Lets call the integral above I.
Then I = residues of .
Then when i find these residues i sub them into to get the residues but i cant figure out what z should be. It SHOULD be and but i have no idea how to get those. I got and . Are those equivalent?!?