Determine whether the set G is a groupunder the operation *

[j9mom]

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?

 

[j9mom]

But I also need to prove then that (ce-df)(ed+ce)=0?

 

[HallsofIvy]

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.