4) Find the integral J: by the complex path (+2at-2a cos e integral ( Residue) method, (Think that lal #1, examine these conditions separately lal >I and lal I the results clepending on a) an Swer

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Q: I hope the solution is understandable and not abbreviated

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A: Cauchy residue theorem is used to find the integral of a closed curve. Cauchy residue theorem says…

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A: Here we replace x by some variable so it makes our integrand easy to solve.

Q: 3) ) What are all the fourth roots of i (that is, i'A)? ser and every z with z" 1, we have f(z) =0…

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Q: MTH3332 ADVANCED THEORY OF COMPLEX FUNCTIONS - MIDTERM - 13.04.2021 z+i dz throughout the contours…

A: See the attachment.

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Q: 215 5. (a) Transform the real integral Pz dr into a complex inte- gral clearly specifying the…

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Q: 21 4) Find the integral Ji by the complex path (+2at-2a cose integral (Residue) method. (Think that…

A: Given ∫02πdθ1+2a2-2a cosθ It can be written as, ∫02πdθ1+2a2+-2a cosθ It is of the form, ∫02πdθa+b…

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Q: Also apply Residue theorem to find the coSTz? value of the integral . C:|z + 1| = 3 (z+1)2(z-2)

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Q: 8.) Consider the contour C in the complex plane consisting of the portion from z = 1 to z = 2+ i. of…

A: A.Now, let's find an antiderivative of z^{2} with respect to z. We have \frac{1}{3}z^{3}+C, where C…