5.30. UITULU eur 5.39. Evaluate z dz when : >0 and C is the circle Izl...
2. Evaluate Scf()dz for the following f() and C f(z) = zz2 and C is the se micircle z = 2e10, 0 a. θ π. b. fz)2an C i the circle lz -il 2. z2+4 2. Evaluate Scf()dz for the following f() and C f(z) = zz2 and C is the se micircle z = 2e10, 0 a. θ π. b. fz)2an C i the circle lz -il 2. z2+4
Q5) Evaluate $c f(z) dz where C is the unit circle Iz| = 1 and f(2) is defined as follows a) f(z) = z2+z2+z_ b) f(x) = tan z c) f() = cosha
Question 1.0 [10 marks] Evaluate dz a. z4+z3-272, With C: Izl = 1 b. J2 cos230 de 5-4cos20 Hint: You may use the following formula without proof, z = e", cos 0 = (z + z^)/2
Find a holomorphic function F(z) on Ω-{z I Izl < r} such that for any a E Ω, F(a) F(0)-Z dz. Suppose f(z) is entire and Ω is simply connected domain. Show lim 22-h2220 Find a holomorphic function F(z) on Ω-{z I Izl
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.
evaluate the following integrals. please show procedure. Develop g(z)= 1/(z-1)(z-2) into a laurent series that is valid for the following anular domains. 4) 23. 01/22 dz Y a) r=1121=5), bydle-il-24 Sol: Ti r = {12-21 = 2 3 4 Sol: Ti 1 5) S dz 23(2-1) 4 r 6) J ze² z ²-1 dz 8=2 Izl=2) Sol: 2li cash (1) Y 9) 0시레시 (o) 0 12-2[J.
5. Evaluate where D is the upper solid hemisphere 2y2+ z2 < 4, z 2 0.
Evaluate the integral. Does Cauchy's theorem apply? Show details . 2 & de 1 6 z dz > ¿ z2+ CZ til: i Z2+1 C: 12-11 Counterclockwile Counter clock wise
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.
Exercises aw the contours γ-[0, i], σ [0, l] + [1,1]. Evaluate re z dz re z dz Exercises aw the contours γ-[0, i], σ [0, l] + [1,1]. Evaluate re z dz re z dz