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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0d0eb9b-5ed0-46d3-a032-d4bf7a7245ca%2F2dd7a1ee-ca8b-4b67-ad4f-b4cfcc2da715%2F5d7zd4_processed.jpeg&w=3840&q=75)
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-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0d0eb9b-5ed0-46d3-a032-d4bf7a7245ca%2F2dd7a1ee-ca8b-4b67-ad4f-b4cfcc2da715%2F90hs2a_processed.jpeg&w=3840&q=75)
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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