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(3+5omega+3omega^(2))^(6)...

`(3+5omega+3omega^(2))^(6)`

A

42

B

48

C

52

D

64

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(3 + 5 omega + 3omega^(2))^(6) =

If 1 , omega + omega^(2) are the cube roots of unity prove that (i) (1 - omega + omega^(2))^(6) + (1 - omega^(2) + omega)^(6) = 128 = ( 1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7) (ii) ( a+ b) ( aomega+b omega^(2))( a omega^(2) + b omega) = a^(3) + b^(3) (iii) x^(2) + 4x + 7 = 0 " where " x = omega - omega^(2) - 2 .

If 1 , omega , omega^(2) are the cube roots of unity prove that (1 - omega + omega^(2))^(6) + ( 1 - omega ^(2) + omega)^(6) = 128 = (1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7)

If omega is a imaginary cube root of unity , then 225 + (3 omega + 8 omega^(2))^(2) + (3 omega^(2) + 8 omega)^(2) =

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)

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

If 1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . ( 1 - omega + omega^(2))^(3)

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

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

(3 - omega) ( 3- omega^(2)) ( 3- omega^(4)) (3 - omega^(8)) =

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

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

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  3. (3+5omega+3omega^(2))^(6)

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

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  5. (1+omega)(1+omega^(2))(1+omega^4)(1+omega^(5))..........2n factors =

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  6. (1+omega)(1+omega^(2))(1+omega^(3))(1+omega^(4))(1+omega^(5))......(1+...

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

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  8. (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)

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

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

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

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

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

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

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

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

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

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  18. (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….....

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

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

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