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If n is a positive integer, then (1+...

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

A

`2^((n//2)+1).cos(npi)/(3)`

B

`2^((n//2)+1).cos(npi)/(4)`

C

`2^((n//2)+1).cos(npi)/(5)`

D

`2^((n//2)+1).cos(npi)/(6)`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. ((1+sintheta+icostheta)/(1+sintheta-icostheta))^(n)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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