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Show that (a) S' = {z = a + bi e C|a, b € R, |2| = a² + b² = 1} is a subgroup of C*. (b) SO2(R) = {|| cos e - sin e sin 0 cos e | 10ER} is a subgroup of GL2(R). (c) S' = SO2(R). Hint: cos(a+ 3) = cos a cos 3 – sina sin 3 and sin(a + B) = sin a cos 3 + cos a sin 3 %3D

Show that (a) S' = {z = a + bi e C|a, b € R, |2| = a² + b² = 1} is a subgroup of C*. (b) SO2(R) = {|| cos e - sin e sin 0 cos e | 10ER} is a subgroup of GL2(R). (c) S' = SO2(R). Hint: cos(a+ 3) = cos a cos 3 – sina sin 3 and sin(a + B) = sin a cos 3 + cos a sin 3 %3D

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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Show that (a) S' = {z = a + bi e C|a, b € R, |2| = a² + b² = 1} is a subgroup of C*. (b) SO2(R) = {|| cos e - sin e sin 0 cos e | 10ER} is a subgroup of GL2(R). (c) S' = SO2(R). Hint: cos(a+ 3) = cos a cos 3 – sina sin 3 and sin(a + B) = sin a cos 3 + cos a sin 3 %3D
Transcribed Image Text:Show that (a) S' = {z = a + bi e C|a, b € R, |2| = a² + b² = 1} is a subgroup of C*. (b) SO2(R) = {|| cos e - sin e sin 0 cos e | 10ER} is a subgroup of GL2(R). (c) S' = SO2(R). Hint: cos(a+ 3) = cos a cos 3 – sina sin 3 and sin(a + B) = sin a cos 3 + cos a sin 3 %3D
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