Question

Consider the contour integral

∮ c 1/1+z ⁴ dz
Where the contour c is a semicircle of radius R

Answer 1

To evaluate the given contour integral using the Residue Theorem, we need to find the residues of the function 1/(1+z⁴) at its singularities, which are the fourth roots of -1, and apply the Residue Theorem.

Step-by-step explanation:

The given question is about the contour integral: ∮c 1/(1+z⁴) dz, where the contour c is a semicircle of radius R. To evaluate this integral, we can use the Residue Theorem. We need to find the residues of the function 1/(1+z⁴) at its singularities, which are the fourth roots of -1. Once we find the residues, we can apply the Residue Theorem to evaluate the contour integral.