What is the image of the unit disk under the map w log z? What is the image of the unit disk under the map w log z?
2. (10pts) Find a biholomorphic map between the unit disk A and the region U = {z €C10 < Arg(z) <5).
(d) Sketch the image under the function f(z) Logz of the region (s : 비 > 1,0 etch the image under the function f(2)Log 2 of the region Arg: ST/2) (d) Sketch the image under the function f(z) Logz of the region (s : 비 > 1,0 etch the image under the function f(2)Log 2 of the region Arg: ST/2)
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). This problem involves the mapping w(z)-,(z + z") between the z-plane and the w-plane. The two parts can be solved independently. 2 (a). Identify all of the values of z for which the mapping w(z) fails to be conformal. In each case, explain why the mapping is not conformal at that value of z. (b). Find the image in the w-plane of the unit circle Iz1, Graph it, label the axes, and label the w-plane points that correspond to...
(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...
use a karnaugh map to minimize and draw the logic diagram f(w,x,y,z)=w',x',y',z'+wxy'z'+wxyz=w'xyz'+wxyz'
36. The quarter-disk Izl < 1, x > 0, y > 0 onto the exterior of the unit circle |w| = 1. 36. The quarter-disk Izl 0, y > 0 onto the exterior of the unit circle |w| = 1.
Simple Möbius. semi-disk z<1 with Imz> 0 onto the first quadrant Re w is mapped Find a Möbius transformation w (azb)/(cz d) that maps the 0 with Im w> 0 such that z = -1 0 and z 1 is mapped onto the point at infinity. Also find the inverse f(2) onto w transformation. Simple Möbius. semi-disk z 0 onto the first quadrant Re w is mapped Find a Möbius transformation w (azb)/(cz d) that maps the 0 with Im...
solution to 2 (ii) Show that the image of f is not a subspace of R 2. Let U, V, and W be vector spaces over the field k, and let f: Ux V- W be a bilinear map. Show that the image of f is a union of subspaces of W. 3. Let k be a field, and let U, V, and W be vector spaces over k. Recall that (ii) Show that the image of f is not...
7.2.1 Calculate the Gauss map of the paraboloid , with equation 2y2. What is the image of G? 7.2.1 Calculate the Gauss map of the paraboloid , with equation 2y2. What is the image of G?