Question 1144065: show that the set of complex numbers under multiplications is a GROUP. Find Re(z^-1).
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
show that the set of complex numbers under multiplications is a GROUP. Find Re(z^-1).
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For your info :
The set of ALL complex numbers under multiplication IS NOT A GROUP, since the zero element HAS NO inverse.
So, the statement in the post is FATALLY INCORRECT.
The correct statement is THIS :
The set of all non-zero complex numbers under multiplication is a GROUP.
For the proof, see, for example, this Internet page
https://proofwiki.org/wiki/Non-Zero_Complex_Numbers_under_Multiplication_form_Abelian_Group
or any standard university textbook in Abstract Algebra.
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The students' folklore says that if in an exam a student pronounces the phrase as it is printed originally in this post,
then a professor who takes this exam will award him (or her) the lowest possible score immediately.
It is very simple and popular test to check if the student knows the basics of Abstract Algebra.
So, be aware (!)
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