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If n is a positive integer and (1+i)^(2n...

If n is a positive integer and `(1+i)^(2n)+(1-i)^(2n)=kcos(npi//2)` then the value of k is

A

`2^n`

B

`2^(n-1)`

C

`2^(n+1)`

D

1

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
  1. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then x/y-y/x=

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

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

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

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

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

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

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

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

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

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  11. Two of the three values of (-1)^(1//3) are cos(pi//3)+isin(pi//3),cos(...

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  12. One value of (1+i)^(1//2) is 2^(1//4)e^(ipi//8).The other value is

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  13. If z+1/z=1 and z be any complex number,then the value of z^(99)+(1)/(z...

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  14. If (sqrt3-i)^n=2^n,b epsilon 1,the set of integers,then n is a multipl...

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  15. If A+B+C=180^@ and cis A=x,cis B=y,cis C=z, them xyz=

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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 zk=cos((kpi)/(10))+isin((kpi)/(10)) , then z1z2z3z4 is equal to

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  18. The general value of theta which satisfies the equation (costheta+isin...

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  19. sum(k=1)^6[sin((2kpi)/(7))-icos((2kpi)/(7))]=

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  20. The value of prod(k=1)^6((sin)(2pik)/(7)-(icos)(2pik)/(7)) is

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