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(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 0 cos 0 | 0 E R} is a subgroup of GL2(R). sin 0 (c) S' = SO2(R). Hint: cos(a + B) = cos a cos B – sin a sin 3 and sin(a + B) = sin a cos 3 + cos a sin 3 -

(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 0 cos 0 | 0 E R} is a subgroup of GL2(R). sin 0 (c) S' = SO2(R). Hint: cos(a + B) = cos a cos B – sin a sin 3 and sin(a + B) = sin a cos 3 + cos a sin 3 -

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