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) = {|10 €R is a subgroup of GL2(R).sin 0cos O(c) S' = SO2(R).Hint: cos(a + B)= cos a cos ß – sin a sin ß and sin(a +B) = sin a cos 3 + cos a sin 3

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Answered: Show that (a) S' = {z= a + bi E C|a, b…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 1E: Let H1={ [ 0 ],[ 6 ] } and H2={ [ 0 ],[ 3 ],[ 6 ],[ 9 ] } be subgroups of the abelian group 12 under...

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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) = {| 10 €R is a subgroup of GL2(R). - sin 0 cos 0 (c) S' = SO2(R). Hint: cos(a + B) = cos a cos ß – sin a sin 3 and sin(a + B) = sin a cos 3+ cos a sin 3