Let S = {a+bie C: a,b € R, a² + b² = 1} be the set of all complex numbers of modulus 1. Prove that S is a subgroup of the multiplicative group C.
Let S = {a+bie C: a,b € R, a² + b² = 1} be the set of all complex numbers of modulus 1. Prove that S is a subgroup of the multiplicative group C.
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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![(b) Let
S = {a+bie C : a, b € R, a² + b² = 1}
be the set of all complex numbers of modulus 1. Prove that S is a subgroup of
the multiplicative group CX.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f55c31f-0fa5-4801-b176-ab5473ae935b%2Fa9dffec9-53a6-4397-9150-6e4be2cadf5d%2Fp62xdld_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Let
S = {a+bie C : a, b € R, a² + b² = 1}
be the set of all complex numbers of modulus 1. Prove that S is a subgroup of
the multiplicative group CX.
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