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Prove that C*, the group of nonzero complex numbers under
Chapter 4, Problem 27E(choose chapter or problem)
QUESTION:
Prove that C*, the group of nonzero complex numbers under multiplication, has a cyclic subgroup of order \(n\) for every positive integer \(n\).
Questions & Answers
QUESTION:
Prove that C*, the group of nonzero complex numbers under multiplication, has a cyclic subgroup of order \(n\) for every positive integer \(n\).
ANSWER:Step 1 of 4
Given: The group of non-zero complex numbers under multiplications, \(C^{*}\) is a group.
The objective is to prove that \(C^{*}\) has a cyclic subgroup of order \(n\), for every positive integer \(n\).