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(1-omega+omega^(2))(1-omega^(2)+omega^(4...

`(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-omega^(8)+omega^(16))`

A

4

B

8

C

12

D

16

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(1+omega-omega^(2))(1-omega+omega^(2))

(1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))(1-omega^(7))(1-omega^(8))

(1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)

(2+omega^(2)+omega^(4))^(5)

(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….. to 2n factors

(1 - omega + omega^(2)) ( 1 - omega^(2) + omega^(4)) ( 1- omega^(4) + omega^(8)) to 2n factors =

Arrange the following values in descending order A)(1+omega)(1+omega^2)(1+omega^4)(1+omega^8) B) (1-omega+omega^2)^7+(1+omega-omega^2)^7 C)(1-omega)(1-omega^2)(1-omega^4)(1-omega^8) D) (1-omega+omega^2)(1-omega^2+omega^4)

(1 - omega) (1 - omega^(2)) (1 - omega^(4)) (1 - omega^(5)) (1 - omega^(7)) (1 - omega^(8)) =

(1-omega+omega^(2))^(7)+(1+omega-omega^(2))^(7)

(1+omega)(1+omega^(2))(1+omega^(3))(1+omega^(4))(1+omega^(5))......(1+omega^(3n))

DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. If x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega then xyz

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  2. If a, b are real and x=a+b,y=aomega^(2)+bomega,z=aomega+bomega^(2)" th...

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  3. (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-om...

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  4. If 1 , omega , omega^(2) are the cube roots of unity, then prove that ...

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  5. (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….....

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  6. If omega is a complex cube root of unity then omega^((1/3+2/9+4/27+......

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  7. (a+bomega+comega^(2))/(c+aomega+bomega^(2))

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  8. (1)/(1+2omega)-(1)/(1+omega)+(1)/(2+omega)

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  9. If omega is a complex cube root of unity, then sin[(omega^(10)+omega^(...

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  10. If 1,omega,omega^(2) are the cube roots of unity and alpha=omega+2omeg...

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  11. If alpha, beta are the roots of 1 + x + x^(2)= 0, then the value of al...

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  12. If x^(2) + x + 1 =0 , then the value of (x + (1)/(x))^(2) + (x^(2) + ...

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  13. If the cube roots of unity are 1,omega,omega^(2) then the roots of the...

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  14. If alpha, beta are the non-real cube roots of 2, then alpha^(6)+beta^...

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  15. If alpha is a non-real root of x^(6)-1=0 then (alpha^(5)+alpha^(3)+alp...

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  16. If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+...

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

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

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  19. 1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...

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

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