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c) Show that the image of the annulus {z: ^< 121 <2} under W = 1 is the domain {W: Rew > - 1, 1 w - 3/31 > 1 } 2

c) Show that the image of the annulus {z: ^< 121 <2} under W = 1 is the domain {W: Rew > - 1, 1 w - 3/31 > 1 } 2

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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Questions 1c and 1dii please 1c ~ “Show that the image of the annulus”
Z-2 4z 1) a) show that the image of the disc 12-1/2 under the Möbius transformation w= Z+1 is the domain & WEC | IW-2)>2} b) Show that the image of the domain &z: Rez <1} under the Mobius transformation w= Z+1 is the domain & W: IW-31> 1 } c) Show that the image of the annulus {z: ^<12/<2} under W = z² = 1 is the domain {W: Rew >-1, 1w - 3/31 > 33 3 d) Find the Möbius transformation that maps. 8 i) 0±0, 1-i →2-2i, i→1; ii) is 0, -36+2i, ∞ >2i
Transcribed Image Text:Z-2 4z 1) a) show that the image of the disc 12-1/2 under the Möbius transformation w= Z+1 is the domain & WEC | IW-2)>2} b) Show that the image of the domain &z: Rez <1} under the Mobius transformation w= Z+1 is the domain & W: IW-31> 1 } c) Show that the image of the annulus {z: ^<12/<2} under W = z² = 1 is the domain {W: Rew >-1, 1w - 3/31 > 33 3 d) Find the Möbius transformation that maps. 8 i) 0±0, 1-i →2-2i, i→1; ii) is 0, -36+2i, ∞ >2i
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