(5 points.) Let C be the positively oriented circle of radius 2 around the origin. The mapping w ...
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...
please solve these two questions completely with steps thank you! 2. Find the image of a horizontal line under the mapping w e Problem 5. Evaluate the following integrals, justifying your procedures. 1. e z, where C is the circle with radius, Centre 1,positively oriented. 2. Let CRbe the circle ll R(R> 1), described in the counterclockwise direction. Show that Log Problem 6. The function g(z) = Vre2 (r > 0,-r < θπ) is analytic in its domain of definition,...
5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify 5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify
15. Let F(z,y)- F dr where C is any positively-oriented Jordan curve that encloses the origin Evaluate 15. Let F(z,y)- F dr where C is any positively-oriented Jordan curve that encloses the origin Evaluate
Evaluate line integral ( F. dr where C is any positively oriented simple closed curve that encloses the origin by using a circle of radius r, and r is small enough so that the circle lies entirely inside C given F(x, y) = ? 1)_ 2xyi +(y2 – xº)j Ans (x² + y²)
We say that zois a source or a sink for a given flow f(2) if there exists a circle around it such that the contour integral of f(z) around this positively oriented circle is purely imaginary with imaginary part positive or respectively negative. Alternatively, we say that zois a positive or negative vortex for a given flow if there exists a circle around it such that the contour integral of f(z) around this positively oriented circle is real positive or...
(20 points) Let and let C' be any simple closed curve in a plane oriented counterclockwise. Please show that the only two possible values for F. dr is 0 or-2π. (Hint) The domain of the vector field does not include the origin. Hence, the origin is seen as a hole. Consider 1) Curve C does not encompass the origin. 2) Curve C does encompass the origin. In this case, use an auxiliary curve that encompasses the origin and is encompassed...
Evaluate the integral 3,3 + 2 where C is the positively oriented circle 2-22
1 3. Let f(x) = 22(2-2)(2 - 4) and C a circle of radius 2k - 1 about the origin with counterclockwise orientation. (1) Find (2) Find 50, 5(=dz. Je_1(a) dz. 5. 1(a) dz. (3) Find
- 50ST. Show that Let C be a positively oriented curve given by z = 20 + Re 5) when n = +, +2,. 2ni when n = 0. (z- 20)-dz = %3D %3D