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4. Show that the ratio of areas is invariant in the geometry (C, G)

4. Show that the ratio of areas is invariant in the geometry (C, G)

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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Question 2 Let G = {T(z) = az + bž + c: a, b, c E C, Ja| # b|}. 1. Show that (C, G) is a geometry in the sense of Felix Klein. 2. Show that every T E G sends straight lines to straight lines. 3. Show that all triangles in the complex plane are congruent in the geometry (C,G). 4. Show that the ratio of areas is invariant in the geometry (C, G)
Transcribed Image Text:Question 2 Let G = {T(z) = az + bž + c: a, b, c E C, Ja| # b|}. 1. Show that (C, G) is a geometry in the sense of Felix Klein. 2. Show that every T E G sends straight lines to straight lines. 3. Show that all triangles in the complex plane are congruent in the geometry (C,G). 4. Show that the ratio of areas is invariant in the geometry (C, G)
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