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4. Find a Möbius transformation which maps the region outside the unit circle onto the left- half plane. What are the images of circles |z| = r > 1? And the images of lines passing through the origin?

4. Find a Möbius transformation which maps the region outside the unit circle onto the left- half plane. What are the images of circles |z| = r > 1? And the images of lines passing through the origin?

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 4 and answer is attached
C) CONFORMAL MAPPINGS 1. T(0) = -1. z+i = -i- 3i 3i T(2) = -i- z+i 2. T(2) = – or 2- 2 or T(2) = =2, 3. T(2) = ; The line is mapped onto the circle Jw +1 – i| = 1 or |w – 1 – i| = 1, respectively. 1+2 4. For example T(2) = Circles |2| =r>1 are mapped onto circles in the left half-plane. Lines crossing the origin are mapped onto circles passing through ±1, with the exception of the re al axis which is mapped onto the real axis.
Transcribed Image Text:C) CONFORMAL MAPPINGS 1. T(0) = -1. z+i = -i- 3i 3i T(2) = -i- z+i 2. T(2) = – or 2- 2 or T(2) = =2, 3. T(2) = ; The line is mapped onto the circle Jw +1 – i| = 1 or |w – 1 – i| = 1, respectively. 1+2 4. For example T(2) = Circles |2| =r>1 are mapped onto circles in the left half-plane. Lines crossing the origin are mapped onto circles passing through ±1, with the exception of the re al axis which is mapped onto the real axis.
4. Find a Möbius tran sformation which maps the region outside the unit circle onto the left- half plane. What are the images of circles |2| = r > 1? And the images of lines passing through the origin?
Transcribed Image Text:4. Find a Möbius tran sformation which maps the region outside the unit circle onto the left- half plane. What are the images of circles |2| = r > 1? And the images of lines passing through the origin?
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