Example 3: Find the bilinear transformation that maps the points (o, i, 0) into the points...
(a) Find the bilinear transformation that maps the point (0), (1), (i) into the point (1+i), (-i), (2-1). (b) Show that the function sinhz is an analytic function. 42-3 Where C is the circle such that Evaluate the integral Sc(2-2) (1) C:Z1 = 1 (2) C:[Z= 1 (3) C:Z) = 3 200
(Bilinear transformation and all pass systems in the Laplace domain). The bilinear transformation F:C→C is a mapping from the z-domain to the Laplace domain, defined as s唔倫-1) without loss of generality, let us 7 17-) Without loss of generality, let us Td 1+z-1 assume that the scaling factor Ta is not important here, so we can choose 1-z-1 Ta = 2 to simplify our discussions; hence, s(z) =-. 1+z-1 (a) Show that the transformation maps the unit circle in the...
(2) (8 points) Find the linear fractional transformation w = T(-) that maps points {0, 1, 00} to points {0, 0, 2), respectively.
find the bilinear trasnformation that maps the point 1+i,-i,2-i of the z plane into the points 0,1,i of the w plane
(a) Find a Möbius transformation that maps 0 to, 1 to 2, and -1 to 4 (b) Let h(z)be the Möbius transformation and C: z-21 2 be the circle 2z-8 with centre 2 and radius 2. Determine the image of the interior of the circle C under h(z). (a) Find a Möbius transformation that maps 0 to, 1 to 2, and -1 to 4 (b) Let h(z)be the Möbius transformation and C: z-21 2 be the circle 2z-8 with centre...
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...
(c) please Tz that 1. Find the most general linear fractional transformation w = maps the region A into B : (a) A = {l-1 <1}, B = {Im w >0} (6) A = {lz| <1}, B= {Rew >0} (c) A = {]z – al < R}, B = {Rew 5-3}
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
please answer both. thanks 5. Find the unique Möbius transformation that sends 1 Hii H-1, and -1H-i. What are the fixed points of this transformation? What is T(0)? What is T(0o)? 14. Find a Möbius transformation that takes the circle |z1 = 4 to the straight line 3x + y = 4. Hint: Track the progress of three points, and the rest will follow.
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto