Show that under the transformation w = 1 (a) the image of lines y = x –1 and y = 0 are the circle u? + v² in z space and the others in w space and determine the corresponding directions along them. (c) Verify the conformality of the mapping at the point zo = 1. - u – v = 0 and the line v = 0 respectively. (b) Sketch the two lines

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 61E
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12. Show that under the transformation w =
1
(a) the image of lines y = x – 1 and y = 0
are the circle u? + v² – u - v = 0 and the line v = 0 respectively. (b) Sketch the two lines
in z space and the others in w space and determine the corresponding directions along them.
(c) Verify the conformality of the mapping at the point zo = 1.
Transcribed Image Text:12. Show that under the transformation w = 1 (a) the image of lines y = x – 1 and y = 0 are the circle u? + v² – u - v = 0 and the line v = 0 respectively. (b) Sketch the two lines in z space and the others in w space and determine the corresponding directions along them. (c) Verify the conformality of the mapping at the point zo = 1.
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