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Determine whether the set G is a groupunder the operation *

  • Thread starter j9mom
  • Start date
  • #1
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Homework Statement



G={c+di e C| cd =0 and c+d does not =0} a*b=ab

Homework Equations



OK, I know I need to prove closed under *, and associativity and identity and inverse. I was able to do it for other set, but I do not understand what this set is saying



The Attempt at a Solution



OK 1, a=c+di and b=e+fi then a*b = (c+di)(e+fi) =ce-de+edi+cfi = ce-de+(ed+cf)i which is in G so yes

Is that correct?
 

Answers and Replies

  • #2
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But I also need to prove then that (ce-df)(ed+ce)=0?
 
  • #3
HallsofIvy
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It's not clear to me what you are asking. This is hte set of complex numbers a+ bi such that a or[/b\] b but not both are 0. Yes, (a+bi)*(c+ di)= (ac- bd)+ (ad+ bc)i. But you haven't shown that is in the set until you have shown that either ac- bd= 0 or ad+ bc= 0 but not both.
 

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