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If n is a positive integer and (1+isqrt3...

If n is a positive integer and `(1+isqrt3)^(n)+(1-isqrt3)^(n)=2^(n+1)costheta`, then the value of `theta` is

A

`npi//3`

B

`npi//2`

C

`npi//4`

D

none

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then...

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  2. If n is a positive niteger, then (sqrt3+i)^(n)+(sqrt3-i)^(n)

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  3. If n is a positive integer and (1+isqrt3)^(n)+(1-isqrt3)^(n)=2^(n+1)co...

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  4. If n is an integer which leaves remainder one when divided by three, t...

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  5. ((-1+isqrt3)/(2))^(3n)+((-1-isqrt3)/(2))^(3n)

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  6. (1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)

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

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  8. If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

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  9. [(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(...

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  10. If (sqrt3+i)^(100)=2^(99)(a+ib) then b=

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

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

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  13. 4+5(-(1)/(2)+(isqrt3)/(2))^(334)+3(-(1)/(2)+(isqrt3)/(2))^(365)

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  14. ((-1+isqrt3)/(2))^(6)+((-1-isqrt3)/(2))^(6)

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

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

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

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

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

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

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