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2. Find a Möbius tran sformation which maps the region |z -il < 2 onto the upper half plane, the imagin ary axis onto itself, and which fixes the point i.

2. Find a Möbius tran sformation which maps the region |z -il < 2 onto the upper half plane, the imagin ary axis onto itself, and which fixes the point i.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Do problem 2 and answer is attached
C) CONFORMAL MAPPINGS 1. T(0) = -1. 2+i T(2) = -i- 2- 3i 2- 3i T(2) = -i z+ i 2. or T(2) = 23 or T(2) = . 3.
Transcribed Image Text:C) CONFORMAL MAPPINGS 1. T(0) = -1. 2+i T(2) = -i- 2- 3i 2- 3i T(2) = -i z+ i 2. or T(2) = 23 or T(2) = . 3.
2. Find a Möbius tran sformation which maps the region |2 – i| < 2 onto the upper half plane, the imagin ary axis onto itself, and which fixes the point i. 3. A Möbius tran sformation T maps the upper half plane onto itself, and the circle |z–1| = 1 on to the imaginary axis such that the point 1+i maps to i. Compute T. Is T uniquely determined by the given con dition s? What is the imago of the line Im-
Transcribed Image Text:2. Find a Möbius tran sformation which maps the region |2 – i| < 2 onto the upper half plane, the imagin ary axis onto itself, and which fixes the point i. 3. A Möbius tran sformation T maps the upper half plane onto itself, and the circle |z–1| = 1 on to the imaginary axis such that the point 1+i maps to i. Compute T. Is T uniquely determined by the given con dition s? What is the imago of the line Im-
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