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Algebra

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1 Apr 2012 07:58:49 IST

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coplex no.

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

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Tarun Garg

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1 Apr 2012 17:03:44 IST

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WE ARE GIVEN THAT Z=-1+i3^1/2=2/2(-1+i3^1/2) SO IT BECOMES Z=2w........

NOW WE HAVE TO FIND X

WHERE

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

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

THIS IS BY PROPERTY 1+W+W²=0

SO BY ALL THI S WE GET

X=0

Tarun Garg

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Joined: 21 Mar 2012

Posts: 1457

1 Apr 2012 17:04:35 IST

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DONT FORGET TO LIKE IF IT WAS HELPFULLLLLLLLLLLL

shashank shekhar

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2 Apr 2012 19:32:26 IST

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thank u

Tarun Garg

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Joined: 21 Mar 2012

Posts: 1457

2 Apr 2012 19:37:02 IST

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my pleasure

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