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4) a) Find the image of the following under W = Z² 4) The line x = 3 2) The domain 1 b) Let f(z) = ½/ 1) What is the image of the line y = 2 under £? 2) Show that maps the interior of the unit circle in the first quadrant to the exterior of the unit. circle in the fourth quadrant 5) Prove: a) lim Z+di Z-1-21 b) lim 210 c) lim 740 (Im²) ² 121²2² (Rez)² 121 A W = Z d) Compute 2

4) a) Find the image of the following under W = Z² 4) The line x = 3 2) The domain 1 b) Let f(z) = ½/ 1) What is the image of the line y = 2 under £? 2) Show that maps the interior of the unit circle in the first quadrant to the exterior of the unit. circle in the fourth quadrant 5) Prove: a) lim Z+di Z-1-21 b) lim 210 c) lim 740 (Im²) ² 121²2² (Rez)² 121 A W = Z d) Compute 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: 4 part b, question 2 5 part b and c
(4) a) Find the image of the following under W = Z² 4) The line x = 3 2) The domain b) Let f(z) = 1/2 1) What is the image of the line y = 2 under f? 2) Show that w = = maps the interior of the unit circle in the first quadrant to the exterior of the unit. circle in the fourth quadrant (5) Prove: a) lim z+di = 1 Z-1-21 b) lim 710 c) lim 130 2 <y <3 (Im²) ² 1Z₁²2² does not exist (Rez) ² --121- = 0 2 Z²-4 d) Compute lim_22² +21- 2931
Transcribed Image Text:(4) a) Find the image of the following under W = Z² 4) The line x = 3 2) The domain b) Let f(z) = 1/2 1) What is the image of the line y = 2 under f? 2) Show that w = = maps the interior of the unit circle in the first quadrant to the exterior of the unit. circle in the fourth quadrant (5) Prove: a) lim z+di = 1 Z-1-21 b) lim 710 c) lim 130 2 <y <3 (Im²) ² 1Z₁²2² does not exist (Rez) ² --121- = 0 2 Z²-4 d) Compute lim_22² +21- 2931
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