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If z^(2)+z+1=0 where z is a complex numb...

If `z^(2)+z+1=0` where z is a complex number, then the value of
`(z+(1)/(z))^(2)+(z^(2)+(1)/(z^(2)))^(2)+(z^(3)+(1)/(z^(2)))^(2)+..........+(z^(6)+(1)/(z^(6)))^(2)`

A

6

B

12

C

18

D

54

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. If x = cis theta , then find the value of [x^(6) + 1/x^(6)].

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  2. If x+(1)/(x)=2costheta" then "x^(10)+(1)/(x^(10))

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  3. If z^(2)+z+1=0 where z is a complex number, then the value of (z+(1)...

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  4. If z=costheta+isintheta, then (z^(2n)-1)/(z^(2n)+1)

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  5. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)+(y)/(x)

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  6. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)-(y)/(x)

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  7. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x-y)/(x+y)

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  8. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "x^(m).y^(n)+(1)/(x^...

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  9. If p=cos2alpha+isin2alpha,q=cos2beta+isin2beta" then "sqrt(p//q)-sqrt(...

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  10. If x+1/x=2cos alpha,y+1/y=2cos beta, then xy+(1)/(xy)=

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  11. If alphaandbeta are the roots of the equation x^(2)-x+1=0" then "alpha...

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  12. If alphaandbeta are the roots of x^(2)-2x+4=0" then "alpha^(n)+beta^(n...

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  13. If alphaandbeta are the roots of x^(2)-2x+4=0" then "alpha^(n)-beta^(n...

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  14. If alpha,beta are roots of the equation x^(2)-4x+8=0 then for any ninN...

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  15. If alphaandbeta are the roots of x^(2)-2x+4=0, then the value of alpha...

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  16. If x satisfies the equation x^(2)-2xcostheta+1=0, then the value of x^...

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  17. If a=cos4pi//3+isin4pi//3" then "(1+a)^(3n)

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  18. If cosalpha+cosbeta=0=sinalpha+sinbeta" then "cos2alpha+cos2beta

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  19. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma" then "cos3al...

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  20. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma" then "sin3al...

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