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((sinpi//8+icospi//8)/(sinpi//8-icospi//...

`((sinpi//8+icospi//8)/(sinpi//8-icospi//8))^(8)`

A

-1

B

0

C

1

D

2i

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. If x satisfies the equation x^2-2xcostheta+1=2costheta,then the value ...

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  2. ((costheta+isintheta)^5(cos3theta-isin3theta)^6)/((cos2theta+isin2thet...

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  3. ((sinpi//8+icospi//8)/(sinpi//8-icospi//8))^(8)

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  4. ((1+sintheta+icostheta)/(1+sintheta-icostheta))^(n)

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  5. If ((sqrt3//2+(1//2)i)/(sqrt3//2-(1//2)i))^(120)=p+iq,then

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  6. If n is a positive integer, then (1+i)^n+(1-i)^n=

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  7. Assertion (A) : (sqrt3+i)^6+(sqrt3-i)^6=-128 Reason (R) : If n is ...

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  8. (sqrt3+i)^7+(sqrt3-i)^7=

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  9. (cos""(pi)/(6)+isin""(pi)/(6))^(1//2)+(cos""(pi)/(6)-isin""(pi)/(6))^(...

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  10. One value of (1+isqrt3)^(3//4)+(1-isqrt3)^(3//4) is equal to

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  11. One of the value of [cos(pi//6)-isin(pi//6)]^(11//2)/[cos(pi//6)+isin(...

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

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  13. If x=cisalpha,y=cisbeta" then " x^3y^4-(1)/(x^3y^4)=

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  14. If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)

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  15. cis(pi)/(10).cis(2pi)/(10).cis(3pi)/(10).cis(4pi)/(10)=

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

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

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

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

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

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