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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

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

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: 4b question 2 5 part b and c Written out on paper please.
(4) a) Find the image of the following under W = Z² 4) The line x = 3 2) The domain b) Let $(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 $(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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