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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

`x_(1)+x_(2)+m-1`

B

`x_(1)+x_(2)+x_(3)m=0`

C

`x_(1)x_(2)x_(3)m-1`

D

`x_(1)-x_(2)+x_(3)m=-1`

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity and n i...

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  2. 1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...

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  3. If 1,z1z2,……z(n-1) are the n^th roots of unity, then (1-z1)(1-z2)…..(1...

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

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  5. If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, the...

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

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  7. If X(n)="cos"(pi)/(2^(n))+"isin"(pi)/(2^(n)), then x(1), x(2), x(3)......

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

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

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  10. If z(k)=cos((kpi)/(10))+isin((kpi)/(10)), then z(1)z(2)z(3)z(4) is equ...

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  11. The cube roots of 1+I are

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

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  13. Find all the values of (sqrt3 + i) ^(1/4) .

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

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  15. The product of the values of [cos""(pi)/(3)+isin""(pi)/(3)]^(3//4) is

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

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  17. If x^6+1=0, then x =

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

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  19. The common roots of the equation z^(3)+2z^(2)+2z+1=0,z^(2014)+z^(2015)...

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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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