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[sqrt2(cos56^(@)15+isin56^(@)15')]^(8)...

`[sqrt2(cos56^(@)15+isin56^(@)15')]^(8)`

A

1

B

i

C

16

D

16i

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
  1. [sqrt2(cos56^(@)15+isin56^(@)15')]^(8)

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  2. (cosalpha+isinalpha)^(5)/((sinbeta+icosbeta)^(3))=

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  3. ((cos3theta-isin3theta)^4)/((sin2theta+icos2theta)^5)=

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  4. ((1+costheta+isintheta)/(1+costheta-isintheta))^(n)

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  5. If ((1+costheta+isintheta)/(sintheta+i+icostheta))^(4)=cosntheta+isinn...

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  6. ((1+isqrt3)/(1-isqrt3))^6+((1-isqrt3)/(1+isqrt3))^6=

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

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

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

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  10. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then (x-y)/(x+y)=

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  11. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then x/y-y/x=

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

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  13. If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then...

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  14. If n is positive integer and (1+isqrt3)^n+(1-isqrt3)^n=2^(n+1) cos...

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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. Show that one value of ((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i...

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

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  18. If p=cos2 alpha+isin2 alpha,q=cos2beta+isin2beta then sqrt(p//q)-sqrt(...

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  19. The values of (1-sqrt3i)^(1//3) are

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  20. The product of the four values of (1/2+i(sqrt3)/(2))^(3//4) is

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