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Algebra

New kid on the Block

 Joined: 1 Apr 2012 Post: 28
1 Apr 2012 07:58:49 IST
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Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

If n is a +ve integer but not a multiple of 3 and z=- -1+iroot3 where (i=root-1) then (z^2n+2^n*z^n+2^2n) is equal topleae reply full explaination with stepwise solution

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
1 Apr 2012 17:03:44 IST
2 people liked this

WE ARE GIVEN THAT Z=-1+i31/2=2/2(-1+i31/2) SO IT BECOMES Z=2w........

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NOW WE HAVE TO FIND X

WHERE

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X=Z2n+2nZn+22n=(2W)2n+2n(2W)n+22n=22n(W2n+Wn+1)............

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IF n IS NOT A MUTIPLE OF THREE THEN 1+Wn+W2n=0....(SHOULD BE REMIND AS PROPERTY)

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THIS IS BY PROPERTY 1+W+W2=0

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SO BY ALL THI S WE GET

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X=0

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
1 Apr 2012 17:04:35 IST
1 people liked this

DONT FORGET TO LIKE IF IT WAS HELPFULLLLLLLLLLLL

Blazing goIITian

Joined: 1 Apr 2012
Posts: 381
2 Apr 2012 19:32:26 IST
0 people liked this

thank u

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
2 Apr 2012 19:37:02 IST
0 people liked this

my pleasure

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