Questions 1c and 1dii please 1c ~ “Show that the image of the annulus” Z-24z1) a) show that the image of the disc 12-1/2 under theMöbius transformation w= Z+1is the domain & WEC | IW-2)>2}b) Show that the image of the domain &z: Rez <1} under theMobius transformation w=Z+1 is the domain & W: IW-31> 1 }c) Show that the image of the annulus {z: ^<12/<2} underW = z² = 1 is the domain {W: Rew >-1, 1w - 3/31 > 33 3d) Find the Möbius transformation that maps.8i) 0±0, 1-i →2-2i, i→1; ii) is 0, -36+2i, ∞ >2i

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Answered: c) Show that the image of the annulus…

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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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Question

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

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