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Determine whether the set G is a groupunder the operation *

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant 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



    3. 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?
     
  2. jcsd
  3. Nov 17, 2009 #2
    But I also need to prove then that (ce-df)(ed+ce)=0?
     
  4. Nov 17, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    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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