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 Exercise [11.01] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [11.01]
As the associative law holds, expressions such as a(bc) are equal to (ab)c.Hence there is no need to use brackets.
We know
-1=ijk
or-i=i^{2}jk=-jk(as i.i=-1)
ori=jk ...(1)
orji=jjk=-k...(2)(pre-multiplying b/s by j)
Now,
ijk=-1
orijkk=-k(post-multiplying b/s by k)
or-ij=-k
orij=k...(3)
From(2)&(3)

ij=-ji ...(4)

or(jk)j=-ji(substituting i=jk in 4)
orjkj=k(using 2)
orjkjj=kj

orjk=-kj...(5)

orijk=-ikj
or1=ikj
orj=ikjj=-ik...(6)
We havejk=-kj(equation 5)
or(-ik)k=-k(-ik)(substituting j=-ik using 6)
ori=kik
orik=kikk=-ki

orik=-ki...(7)


23 May 2008, 07:34

Joined: 16 Dec 2011, 13:25
Posts: 1
Post Re: Exercise [11.01]
this is an other solution.


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Exercise 11.1.doc [62 KiB]
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21 Mar 2013, 22:34
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