|
|
|
|
|
| Author |
Message |
![[Post New]](/templates/default/images/icon_minipost_new.gif) 15 Jan 2008 10:11:31 IST
|
|
|
SHOW THAT (1-  + 2) ( 1- 2 + 4) (1- 4 + 8 )..........TO 2N FACTORS = 2 N |
|
|
|
15 Jan 2008 10:24:09 IST
|
|
|
1+w+w^2=0
1+w^2=-w
sub in eqn similarly w^4=w therefore 1+w=-w^2,w^8=w^2therfroe(1-w^4+w^8)=(-2w)
(-2w)(-2w^2)(-2w)...........upto2n factors=2^n
hence proved(becuase first two terms becomes 4 hence all terms will become four
|
this reply: 5 points
(with 1 
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
15 Jan 2008 10:24:10 IST
|
|
|
(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.
|
__________________________________________________________________________________________________________
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. |
this reply: 7 points
(with 1
in 2 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
16 Jan 2008 08:54:31 IST
|
|
|
yes the ans comes 22n
see the above method
|
I always like to walk in rain as no one can see me crying there :(
frnds are like diamonds , if u hit them , they don't break but they slip frm ur hands
-----It is better to be hated for what you are than to be loved for what you are not.----
*****wen love and skill work together--expect a masterpiece*****
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
|
|
|
|
|
|
|
Moderation Team
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
