2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.
Question 2. (a) Find all solutions : є C of the equation tan(z) = (1 + iVT)/4. (b) Verify that the solutions you claitm to have discovered do actually satisky the oqatio (c) Evaluate the following contour integral: dz tan(a) - 1-iv7 Question 2. (a) Find all solutions : є C of the equation tan(z) = (1 + iVT)/4. (b) Verify that the solutions you claitm to have discovered do actually satisky the oqatio (c) Evaluate the following contour integral:...
1. Evaluate the complex integral: ∫C [zRe(z) − z¯Im(z)]dz, where C is the line segment joining −1 to i. (z¯ = z bar) 2. Evaluate the complex integral: ∫ C [iz^2 − z − 3i]dz, where C is the quarter circle with centre the origin which joins −1 to i.
1. (а) Using an appropriate contour in the upper half plane, find the integral z-1 dz. (z - i)(z+3i)2 If the contour was closed in the lower half plane, explain how your (b) residue calculation would change.
Evaluate the integral $ 3z + 4)cos z dz, C:12+2i = 1 counterclockwise. z² +4 Integrate $c +436 yosz dz, C:/z+3–2i = 3 counterclockwise. (z +4)
Evaluate the integral 5. Ten dz, where C is the boundary of the square with vertices at the points 0, 1, 1+i and i, with a counter clockwise orientation. What is the integral over the reverse contour?
1. Let P(x) = 22020 – 3:2019 + 22 -3. (b) Compute the contour integral Scof(z)dz with f(z) := 2 fled with f(-) -- 2021 – 222020+2 P2) +, where C (0) is the circle 121 = 8 with positive orientation.
1. (20 points) Let C be any contour from z = -i to z = i, which has positive real part except at its end points. Then, consider the following branch of the power function zi+l; f(3) = 2l+i (1=> 0, < arg z < Now, evaluate the integral Sc f(z)dz as follows: (a) (5 points) First, explain why f(z) does not have an antiderivative on C, but why the integral can still be evaluated. (b) (5 points) Then, find...
(1 point) Evaluate the indefinite integral. cos(/z5) Integral NOTE: Enter arctan(x) for tan-1 z, sin(x) for sin .] to enter all necessary, ( and)!! (1 point) Evaluate the indefinite integral. cos(/z5) Integral NOTE: Enter arctan(x) for tan-1 z, sin(x) for sin .] to enter all necessary, ( and)!!