232sheet5 - 4 under the M¨ obius transformation ω = z z-2...

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B U Department of Mathematics Math 232 Introduction To Complex Analysis Spring 2008 Exercise Sheet 5 1 1. Find a M¨ obius transformation that maps the reqion outside the disc D (1 + i ; 2) to a) the region outside the disc D ( - 1; 3) b) the region defined by Re z < - 1. 2. What is the image of the region 0 < Re z < 1 under the M¨ obius transformation ω = 2 z - 1 z - 1 ? 3. What is the image of the wedge 0 < argz < π/
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Unformatted text preview: 4 under the M¨ obius transformation ω = z z-2 ? 4. Find the image of the annulus A (3; 1; 2) under the M¨obius transformation ω = 1 /z . 5. Sketch the image of the unit circle, | z | = 1 under the mapping f ( z ) = z ( π + Arg z ). This is not a M¨ obius transformation Notes 1 Please visit: http://www.math.boun.edu.tr/deptcourses/math232...
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