Question 1144065
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show that the set of complex numbers under multiplications is a GROUP. Find Re(z^-1). 
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For your info :


<pre>
    The set of ALL complex numbers under multiplication  <U>IS NOT A GROUP</U>,   since the zero element HAS NO inverse.
</pre>


So, the statement in the post is &nbsp;<U>FATALLY &nbsp;INCORRECT</U>.  



The correct statement is  &nbsp;<U>THIS</U> :


<pre>
    The set of <U>all non-zero</U> complex numbers under multiplication is a GROUP.
</pre>


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.



/\/\/\/\/\/\/\/



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 &nbsp;(or her) &nbsp;the lowest possible score immediately.


It is very simple and popular test to check if the student knows the basics of Abstract Algebra.


So, &nbsp;be aware &nbsp;(!)