Abstract Algebra Question please help!! Need help using groups and operators?

Let * be an operator defined on C (complex numbers) by letting (a * b) = |ab|





G2: There is an element e in G such that for all x element in G, we have: e*x = x*e = x (identity element e for * )





inorder for the top equation to be a group it has to satisfy G2, but i know it doesn't, now we need a proof that it doesn't,





| ab| is not just absolute, it is the magnitude, and not to forget this is the complex numbers. so something with (a1 +ia2).......





My question is can someone please please pleaseeeeee help me in writing it, you have to prove it in writing in as much details as possible.





No silly stupid questions, such as you wouldn't learn if you don't solve it your self. JUST IF YOU KNOW IT PLEASE HELP, I know the answer, but I never liked proofs ! pleaseeeeeee help any help is appreciated.





thank you very much. best answer would surely get all the points.

Abstract Algebra Question please help!! Need help using groups and operators?
Let a be any complex number which is not a nonnegative real number (a = -1 will do fine). Now, for any element e, a*e = |ae| is a nonnegative real number, thus not equal to a. So there is no element e such that a*e=e*a=a and thus no identity element for *. Q.E.D.

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