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If x^(2)+x+1=0, then sum(r=1)^(2005)(x^(...

If `x^(2)+x+1=0`, then `sum_(r=1)^(2005)(x^(r)+(1)/(x^(r)))^(3)=`

A

4007

B

4006

C

4005

D

4000

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A
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
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  2. The smallest positive integer n for which (1+i sqrt(3))^(n / 2) is rea...

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  3. If x^(2)+x+1=0, then sum(r=1)^(2005)(x^(r)+(1)/(x^(r)))^(3)=

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  4. If z(1), z(2), z(3) be vertices of an equilateral triangle occurring ...

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  5. If z(1), z(2) are two complex numbers such that Im(z(1)+z(2))=0 and Im...

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  6. If alpha is an imaginary fifth root of unity then log (2)|1+alpha+alph...

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  7. If |z+bar(z)|+|z-bar(z)|=8 then z lies on

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  8. The equation |z+i|-|z-i|=k represents a hyperbola, if

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  9. If |z|=k and w=(z-k)/(z+k), then Re (w)=

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  10. If z is a complex number satisfying z^(4)+z^(3)+2 z^(2)+z+1=0 then |z|...

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  11. If alpha is a non-real fifth root of unity, then 3^(|1+alpha+a^(2)+a^(...

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  12. If alpha is a non-real fourth roots of unity, then the values of alpha...

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  13. If x^(2)-x+1=0 then the value of sum(n=1)^(5)(x^(n)+(1)/(x^(n)))^(2) ...

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  14. If arg (z)lttheta, then arg (-z)-arg (z)=

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  15. If (sqrt(3)-i)^(n)=2^(n), n in Z, then n is a multiple of

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  16. The least positive integer n for which (sqrt(3)+i)^(n)=(sqrt(3)-i)^(n)...

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  17. If w is a complex cube roots of unity, then arg (i w)+arg (i w^(2))=

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  18. If z(2-2 sqrt(3) i)^(2)=i(sqrt(3)+i)^(4) then arg z=

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  19. If ((3)/(2)+(i sqrt(3))/(2))^(28)=3^(14)(x+i y) then (x, y)= (where x ...

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  20. If 1, alpha(1), alpha(2), …., alpha(n-1) are the n^(text (th ) roots o...

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