Answered: 2. Show that (a) S' = {z = a + bi E… | bartleby

Elements Of Modern Algebra

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

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