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

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

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0

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6

C

64

D

128

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

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

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

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

(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))

If 1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . (1 - omega + omega^(2))^(5) + ( 1 + omega - omega^(2))^(5)

DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. (1+omega)(1+omega^(2))(1+omega^(3))(1+omega^(4))(1+omega^(5))......(1+...

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

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  3. (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)

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  4. If omega is a complex cube root of unity, then 225+(3omega+8omega^(2))...

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  5. If omega is a complex cube root of unity, then (x+1)(x+omega)(x-omega-...

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  6. (a-b)(aomega-bomega^(2))(aomega^(2)-bomega)

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  7. (a+2b)^(2)+(aomega+2bomega^(2))^(2)+(aomega^(2)+2bomega)^(2)

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  8. If 1 , omega , omega^(2) are the cube roots of unity , then (a+ b)^(3...

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  9. If x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega then xyz

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

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  11. (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-om...

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

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  13. (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….....

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

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

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  16. (1)/(1+2omega)-(1)/(1+omega)+(1)/(2+omega)

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

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

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

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

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