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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?

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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C) CONFORMAL MAPPINGS 1. T(0) = -1. 2 3i 2. T(z) = -i- z+i z - 3i or T(z) =-2 z + i Z Z 2 3. T(z) = or T(z) = = 2-2 2 The line is mapped onto the circle w+ 1 - i| = 1 1+z 4. For example T(z) = 1-z Circles |z| = r> 1 are mapped onto circles in the are mapped onto circles passing through ±1, with mapped onto the real axis.
Transcribed Image Text:C) CONFORMAL MAPPINGS 1. T(0) = -1. 2 3i 2. T(z) = -i- z+i z - 3i or T(z) =-2 z + i Z Z 2 3. T(z) = or T(z) = = 2-2 2 The line is mapped onto the circle w+ 1 - i| = 1 1+z 4. For example T(z) = 1-z Circles |z| = r> 1 are mapped onto circles in the are mapped onto circles passing through ±1, with mapped onto the real axis.
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?
Transcribed Image Text: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?
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