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Statement-I : If xn=cos(pi//2^n)+isi...

Statement-I :
If `x_n=cos(pi//2^n)+isin (pi//2^n)` then `x_1.x_2.x_3…..=-1`
Statement-II : `x_n=cos(pi//4^n)+isin(pi//4^n)` then `x_1.x_2.x_3…..infty=-1`

A

Only I is true

B

Only II is true

C

Both I and II are true

D

Neither I nor II are true

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The correct Answer is:
A
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AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
  1. If x^6+1=0, then x =

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  2. find the roots x^(11)-x^7+x^4-1=0

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  3. The number of common roots of 15th and of 25th roots of unity are

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  4. The common roots of the equation x^(12)-1=0,x^4+x^2+1=0 are

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  5. The product of all nth roots of unity (n gt 1) is

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  6. The product of the distinct (2n)^(th) roots 1+isqrt3 is

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  7. If alpha is a non real root of x^6=1 then (alpha^5+alpha^3+alpha+1)/(a...

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  8. If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity then (1...

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  9. If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity and n i...

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  10. If alpha is an n^(th) root of unity then prove that 1+2alpha+3alpha^2+...

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  11. Statement-I : ((costheta+isintheta)^5(cos3theta-isin3theta)^6)/((co...

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  12. Statement-I : If xn=cos(pi//2^n)+isin (pi//2^n) then x1.x2.x3…..=-...

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  13. Statement-I : If e^(itheta)=costheta+isintheta then for the DeltaABCe^...

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  14. The ascending order of the values of z1=(1+i)^4,z2=(sqrt3+i)^(12),...

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  15. The descending order of the values of z1=((sqrt3)/(2)i+1/2)^6,z2=(...

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  16. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then match t...

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  17. Match the following. {:("I) "(i)^i=,"a) "ipi//2),("II) "logei=,"b)...

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

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

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  20. p,q,r are distinct cube roots of non-zero complex number z. Let a,b,c ...

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