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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