Question 6 ng problems are based on lectures #15- 20.1.Let C be the upper semicircle with radius 1 centered at z = 2 given by theparametrization z(t)= 2+ e", for 0stST. Evaluate the contour integrar2.Let C be the right-hand semicircle with radius 1 centered at origin given by theparametrization z(1) = e" , for - is.Evaluate the contour integral of f(z)along C for the principal branch of the power function defined by:f(z) = z' = exp(iLog(z)), (z|> 0, – x < Arg(z) < t ).3.Let C be the line segment from -1-i to 3 + i given by the parametrizationz(t) = 2t +1 + it , for –1 3.Without evaluating the integral, show that22203dz <+9)-(2 - 9)25.Let C denote the line segment from z =i to z= 1. Without evaluating the integral,show that4/2Let C be the positively oriented circle centered at the origin with radius r> 1.Without evaluating the integral, show that6.Log(2) dzT + In(r)By finding an antiderivative, evaluate the integral, where the contour is any pathbetween the indicated limits of integration:7.|(2z +i) dz-i

Name: Question 6 ng problems are based on lectures #15- 20.1.Let C be the up
Uploaded: 2024-03-20T07:07:50.000Z
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Description: Question 6 ng problems are based on lectures #15- 20.1.Let C be the upper semicircle with radius 1 centered at z = 2 given by theparametrization z(t)= 2+ e", for 0stST. Evaluate the contour integrar2.Let C be the right-hand semicircle with radius 1 c