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If x(n)=cos((pi)/(4^(n)))+i sin ((pi)/(4...

If `x_(n)=cos((pi)/(4^(n)))+i sin ((pi)/(4^(n)))`, then `x_(1), x_(2), x_(3)....oo` is equal to

A

`(1+isqrt3)/(2)`

B

`(-1+isqrt3)/(2)`

C

`(1-isqrt3)/(2)`

D

`(-1-isqrt3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
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AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. cis(pi)/(10).cis(2pi)/(10).cis(3pi)/(10).cis(4pi)/(10)=

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  2. If xn=cos(pi/2^n)+isin(pi/2^n), then x1 x2 x3......infinity

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  3. If x(n)=cos((pi)/(4^(n)))+i sin ((pi)/(4^(n))), then x(1), x(2), x(3)....

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  4. The continued product of the four values of (1-isqrt3)^(3//4) is

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  5. The continued product of all values of root(5)(4) is

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  6. sum(r=1)^(8)[sin(2pir//9)+icos(2pir//9)]=

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  7. The values of sum(m=1)^(10)[sin(2pim//11)-icos(2pim//11)] is

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  8. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then sin3alph...

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  9. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

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  10. If cos alpha+cosbeta+cosgamma = 0 = sinalpha + sinbeta + singamma then...

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  11. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then sin(2alp...

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  12. If cosalpha+cosbeta+cosgamma=0=sin alpha+sinbeta+singamma then cos^2al...

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  13. If cosalpha+coabeta+cosgamma=0=sinalpha+sinbeta+singamma then cos(alph...

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  14. If a=cisalpha,b=cisbeta,c=cisgamma, and a/b+b/c+c/a-1=0 then cos(alph...

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  15. If A+B+C= pi and cos A+cos B+cos C=0=sin A+sin B+sin C , then sin 3A+...

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  16. The cube roots of 1+I are

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  17. The values of (sqrt3+i)^(1//4) are

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  18. The values of (1+i)^(2//3) are

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  19. All the values of (-i)^(1//3) are given by

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  20. If x^4-1=0 then x=

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