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![[Post New]](/templates/default/images/icon_minipost_new.gif) 15 Jan 2008 10:24:10 IST
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(1 - w + w^2)(1- w^2 + w^4)(1 - w^4 + w^8)............to 2n factors
= ( 1 - w + w^2)(1 - w^2 + w)(1 - w + w^2)..........upto 2n factors
( since, w^4 = w , w^8 = w^2 , w^16 = w.......)
=(-2w)(-2w^2)(-2w)(-2w^2)............to 2n factors
= (2^2w^3)(2^2w^3)(2^2w^3).........upto 2n factors
= 2 ^2n.......proved
Hope it helped.Nudge if not clear.Rate if satisfied.
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From J.R.R. Tolkien's 'The Lord of the Rings':
All that is gold does not glitter
Not all who wander are lost
The old that is strong does not wither,
Deep roots are not reached by frost.
From ashes a fire shall be woken
From shadows a light shall spring
Renewed shall be blade that's broken
The crown less again shall be king. |
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