Question #235094

10)Using Residue theorem evaluate ∮c Z cosh πz/Z^(4)+5Z^(2)+4, where C is |z| = 3.

Expert's answer

To compute this, we can have the function :

This is on the contour:

We let f(z) = cos(z)/(z ^{2} + 8). f(z)

Therefore, analytic on and inside the curve C. This is to say is, the roots of z^{2} + 8 are outside the curve. The integral re-written becomes:

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