2. Evaluate Scf()dz for the following f() and C f(z) = zz2 and C is the se micircle z = 2e10, 0 a...
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
5.30. UITULU eur 5.39. Evaluate z dz when : >0 and C is the circle Izl = 3. 2 Ti I (z2 + 1)
2. Let f(z) be the principal branch of i.е., f(z) exp@ Log(z)}. Co mpute (e)dz where C is the semicircle {et : 0 < θ < π
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.
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
c. Evaluate ,f(z) dz with า the circle of radius 1 centered at the origin and traveled once counterclockwise ˊ们: (1-2 For real twith-1 < t < 1 and +12)-1 Explain why f(:)) has an expansion of the form in C , let f(z) be defined by fG)- a. b. Compute Uo(t), Ui(t), and Uz(t) in terms of t. c. Recalling that t is a real number smaller than 1 in absolute value, find the radius of convergence of this...
get the value of the following integrals where c is the circle (abs)z=3 2 dz e*"dz , donde C (z+, uientes: A) φ 2 dz e*"dz , donde C (z+, uientes: A) φ
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.
4[10 pts]. Let f(z) = u (r,0) + iv(r,0) be analytic in a domain D c C which does not contain the origin. Then do the following ones: (a) Show that rurr(r, θ) + rur(r, θ) + u69(r, θ) 0 for all re® E D. (b) Show that (a) is equivalent to the condition that u is harmonic in D (c) Show that the function (in|e )2-[Arg( a(z) z)]2,-π < Arg(z) < π, 4[10 pts]. Let f(z) = u (r,0)...
(1 point) Evaluate the line integral ScF. dr, where F(x, y, z) = -4xi – 4yj + 5zk and C is given by the vector function r(t) = (sin t, cost, t), osts 31/2. 4