5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equatio...
Evaluate the integral 3,3 + 2 where C is the positively oriented circle 2-22
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
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz, where C is the square with vertices at 2i, 3i, 1+ 3i and 1+2i, in this order. (b) (10 points) sin(22) $c 2+1 where C is the positively oriented (counter-clockwise) triangle with vertices (0,0), (2,0) and (0,5). (c) (10 points) cosh(22) -dz, (3-2) where is the negatively oriented (clockwise) circle centered at (1,1) of radius 2. (d) (10 points) dz, 2-1 where C consist...
(5 points.) Let C be the positively oriented circle of radius 2 around the origin. The mapping w 1/(2(22-1(22-9)) transforms C into a closed curve I. Find the winding number of 1. (5 points.) Let C be the positively oriented circle of radius 2 around the origin. The mapping w 1/(2(22-1(22-9)) transforms C into a closed curve I. Find the winding number of 1.
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
Complex Analysis 1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r and 2, find the principal value of that integral, if it exists. 1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r...
Problem 1. Show that fc f(e)ds -o, where C is the unit circle, positively oriented, and (i) f(z) Log(iz +3)
3. 20 marks] Compute these integrals, with γ a circle of radius 2, Centre at origin, oriented counterclockwise: 2 2z (z-1)3, 22 42 γ ~2 + 8.
Question 13 Consider the iftegral 22 -dz V1 + 23 Which of the following integrals is equivalent to this under the substitution u = 1 + 23? u2 du V1+23 Ta s rudu (x - 1) du Set 3 du yu 1 du yu
2-1/2dz if C is a polygonal line with vertices 2,1 + i,-1 i,-2 (without the segment [-2,2) and z-1/ is a principal value. Hint: consider a particular branch which is analytic on the contour uate the following integrals (all contours are positively oriented): cosh(z) 3 dz if C is a square of vertices 1 ti,-1ti C 2 sin(2) dz if C is a circle 3 2(2,2 2 3 dz if C is a rectangle with sides along the lines x-1,x--1,y...