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6. The Joukowski map is defined by w = f(x) = (²+²) Show that J maps the circle S = {|z| = ro} (ro > 0, ro #1) onto an ellipse+ the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z. = 1 and

6. The Joukowski map is defined by w = f(x) = (²+²) Show that J maps the circle S = {|z| = ro} (ro > 0, ro #1) onto an ellipse+ the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z. = 1 and

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 7RE
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Question
6. The Joukowski map is defined by w = f(2) = (2+ Show that J maps the circle S = {[2] = ro} (ro> 0, ro #1) onto an ellipse+ = 1 and the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z.
Transcribed Image Text:6. The Joukowski map is defined by w = f(2) = (2+ Show that J maps the circle S = {[2] = ro} (ro> 0, ro #1) onto an ellipse+ = 1 and the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z.
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