14. What is the image of the upper half-plane under a mapping of the form az + b a, b, c, d real;...
(Complex analysis)
Exercise 6 a) Show that the image of the half-plane y > c (c = const) in the z-plane 1 under the inversion mapping w--s the interior of a circle provided that C0 the inversion mapping w hen0? the inversion mapping w = z when c < 0? b) What is the image of the half-plane y > c (c -const) in the z-plane under c) What is the image of the half-plane y > c (cconst) in...
2. Find the image of the upper half-plane by the mapping 1-χα 1 za where 0< α< 1 and 20 has its principal value.
Problem 1.Use Schwarz - Christoffel Formula Theorem to describe the image of the upper half-plane y 2 0 under the conformal mapping w- f(z) that satisfies the given conditions.C ping w = f(z) that satisfies the given conditions. (Do not try to solve for f(z).) a.) f(z) (z +1)1 b) f,(z) = (z + 1)-1/2(z-1)1/2, f(-1) = 0,f(1) = 1 n12(-1)-14, f(-1)-i,f(0) - o,f(1)-1
Problem 1.Use Schwarz - Christoffel Formula Theorem to describe the image of the upper half-plane y...
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working.
(7) Let 0くa 〈 b 〈 c 〈...
Solve the following questions using confomal mapping from
complex analysis
7.1 Compute the images of the real and imaginary axes and (a) the lower half-plane under the map f(z) = (2+2)/(z-i), (b) the right half-plane under the map f(z) (z 1)/(z +1), (c) the left half-plane under the map f(z) = (z+ 1)/(2-1)
7.1 Compute the images of the real and imaginary axes and (a) the lower half-plane under the map f(z) = (2+2)/(z-i), (b) the right half-plane under the...
Let 0< a<b<e<d for a, b, c, d E R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation x=au + bu, y=cu + dv. (a) Sketch D in the r-y plane for the case ad -bc > 0. (a) Sketch D in the r-y plane for the case ad bc < 0. (c) Calculate the area of D. Show all working.
Let 0
(7) Let 0 < a < b < c 〈 d for a,b,c,de R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation ( d -bc > 0. a) Sketch D in the x-y plane for the case a -bc< (a) Sketch D in the r-y plane for the case ad 0. (c) Calculate the area of D. Show all working.
(7) Let 0
(Complex Analysis)
The linear mapping wFUz+p, where α, β e C maps the point ZFI+1 to the point wi-i, and the poin to the point w2-1i a) Determine α and β. b) Find the region in the w-plane corresponding to the upper half-plane Im(z) 20 in 9. the z-plane. Sketch the region in the w-plane. c) Find the region in the w-plane corresponding to the disk Iz 2 in the z-plane d) Find the fixed points of the mapping
The...
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,...
Let 0 < a <b<e<d for a, b, c, d E R. Consider the set S={(u, ujo < u < 1, 0<u<1) and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the r-y plane for the case ad - be>0. (a) Sketch D in the r-y plane for the case ad - be < 0. (c) Calculate the area of D. Show all working.