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If n is a multiple of 3, then ((-1+isqrt...

If n is a multiple of 3, then `((-1+isqrt3)/(2))^(n)+((-1-isqrt3)/(2))^(n)`

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1

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2

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3

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4

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. If (sqrt3+i)^(100)=2^(99)(a+ib) then b=

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  2. A value of n such that ((sqrt3)/(2)+(i)/(2))^(n)=1 is

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  3. If n is a multiple of 3, then ((-1+isqrt3)/(2))^(n)+((-1-isqrt3)/(2))^...

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  4. 4+5(-(1)/(2)+(isqrt3)/(2))^(334)+3(-(1)/(2)+(isqrt3)/(2))^(365)

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  5. ((-1+isqrt3)/(2))^(6)+((-1-isqrt3)/(2))^(6)

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  6. If n is an integer and z=-1+isqrt3," then "z^(2n)+2^(n).z^(n)+2^(2n)

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  7. If theta=pi//6 then the 10th term of the series 1+(costheta+isintheta)...

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  8. If x = cis theta , then find the value of [x^(6) + 1/x^(6)].

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

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

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

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

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

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

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

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

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

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

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

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

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