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If theta=pi//6 then the 10th term of the...

If `theta=pi//6` then the 10th term of the series `1+(costheta+isintheta)+(costheta+isintheta)^(2)+......` is

A

i

B

`-1`

C

1

D

`-i`

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If theta=pi/6, then the 10th term of the series 1+(costheta+isintheta)+(cos theta+i sin theta)^2+ …. Is

(1-costheta+isintheta)^(6)

(1-costheta+isintheta)/(1+costheta-isintheta)

(1-costheta+isintheta)^6 =

(1-costheta+isintheta)^8 =

(1+costheta-isintheta)^4 =

(costheta+isintheta)^(10)+(costheta-isintheta)^(10)

((1+costheta+isintheta)/(1+costheta-isintheta))^(n)

|1+costheta+isintheta|=

(1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)

DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. ((-1+isqrt3)/(2))^(6)+((-1-isqrt3)/(2))^(6)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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