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(c) please Tz that 1. Find the most general linear fractional transformation w = maps the...
(2) (8 points) Find the linear fractional transformation w = T(-) that maps points {0, 1, 00} to points {0, 0, 2), respectively.
Problem 2. (18 points) (a) Find a fractional linear transformation that maps the right half-plane to the unit disk such that the origin is mapped to -1. (b) A fixed point of a transformation T is one where T(2) = 2. Let T be a fractional linear transformation. Assume T is not the identity map. Show T has a most two fixed points. (c) Let S be a circle and 21 a point not on the circle. Show that there...
z+1 The linear fractional transformation shown below is related to w = u + jv and z = x + jy w= z-2' a. Calculate the curves that the lines v = constant maps to in the x-y plane, b. Calculate the curves that the lines y = constant maps to in the u-v plane, c. What is the line in the x-y plane that maps to a line in the u-v plane?
7. Consider the fractional linear transformation that maps -1 to -2i, 1 to i and i to 0. Determine the image of the unit circle EC 1 the image of the open unit disk (z EC<1), and the image of the interval [-1,1 on the real axis Illustrate with a sketch
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
1. Show that w = 2 + the w-plane. NI maps the half circle | 2 = 1,0 <<n in the z-plane to the line segment -2<u<2 in
Problem 1. Make a sketch of the infinite strip 0< < 1. Then, find and sketch its image under the transformation w-12. În all these problems, z x + iy.
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...
(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...
Help with detail answer. Consider the following: w g(z)where w is the fractional linear (Mobius) transformation Describe and sketch the image set of g(B) if B is the annulus { z ε ¢ : 1 < Izi < 2} Consider the following: w g(z)where w is the fractional linear (Mobius) transformation Describe and sketch the image set of g(B) if B is the annulus { z ε ¢ : 1