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Z-2 1) a) show that the image of the disc 12-1/2 under the Möbius transformation w = 2+1 is the domain & WEC | (W-2)>2} b) Show that the image of the domain {z: Rez < 1} under the Möbius transformation w = 42 is the domain & W: IW-31>13 c) Show that the image of the annulus {z: ^<12/<2} under W = = = 1 is the domain & W: Rew >-1, 1W- 3 3 1> 1 } d) Find the Möbius transformation that maps. Z+1 >> i) 0-0, 1-i→ 2-di, i+1; ii) iso, -3-6+2i, * >2i

Z-2 1) a) show that the image of the disc 12-1/2 under the Möbius transformation w = 2+1 is the domain & WEC | (W-2)>2} b) Show that the image of the domain {z: Rez < 1} under the Möbius transformation w = 42 is the domain & W: IW-31>13 c) Show that the image of the annulus {z: ^<12/<2} under W = = = 1 is the domain & W: Rew >-1, 1W- 3 3 1> 1 } d) Find the Möbius transformation that maps. Z+1 >> i) 0-0, 1-i→ 2-di, i+1; ii) iso, -3-6+2i, * >2i

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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1c) and d) ii) please

Z+1 z-2 1) a) show that the image of the disc 12-1/2 under the Möbius transformation w= is the domain & WEC/ (W-2)>2} b) Show that the image of the domain &z: Rez <1} under the Möbius transformation W = 124 is the domain & w: IW-31>1} c) Show that the image of the annulus {z: ^<12/<2} under W = = = 1 is the domain { W: Rew > - 1, 1 w - 3/31 > 4 3 3 2 4z d) Find the Möbius transformation that maps. i) 0-0, 1-i→ 2-di, i→1; u) iso, -3-6+2i, ∞ >2i
Transcribed Image Text:Z+1 z-2 1) a) show that the image of the disc 12-1/2 under the Möbius transformation w= is the domain & WEC/ (W-2)>2} b) Show that the image of the domain &z: Rez <1} under the Möbius transformation W = 124 is the domain & w: IW-31>1} c) Show that the image of the annulus {z: ^<12/<2} under W = = = 1 is the domain { W: Rew > - 1, 1 w - 3/31 > 4 3 3 2 4z d) Find the Möbius transformation that maps. i) 0-0, 1-i→ 2-di, i→1; u) iso, -3-6+2i, ∞ >2i
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