Define with . Show that N is multiplicative. I'm a bit rusty on this, showing it is multiplicative means closure, associative, inverse, identity, right? Or N(ab) = N(a)N(b)?
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Originally Posted by tttcomrader Define with . Show that N is multiplicative. I'm a bit rusty on this, showing it is multiplicative means closure, associative, inverse, identity, right? Or N(ab) = N(a)N(b)? You need to show that N((a+bw)(c+dw)) = N(a+bw)N(c+dw).
Alright, that would be easy, thank you!
I was trying to work this out, but here is what I got. Let x=a+bw and y=c+dw. N(xy) = N(ac+adw+cbw+bdw), I can't get it into a the form of u+vw, how would I do it? Thanks.
Originally Posted by tttcomrader I was trying to work this out, but here is what I got. Let x=a+bw and y=c+dw. N(xy) = N(ac+adw+cbw+bdw), I can't get it into a the form of u+vw, how would I do it? Thanks. If x=a+bw and y=c+dw then . But , so . Thus . You need to verify that this is equal to . Good luck!
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