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(1+omega)(1+omega^(2))(1+omega^(5))........

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

A

0

B

1

C

`-1`

D

2

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The correct Answer is:
B
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(1+omega)(1+omega^(2))(1+omega^4)(1+omega^(5))..........2n factors =

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(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

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

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

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

AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. If n is an integer and not a multiple of 3 then omega^(n) + omega^(2n...

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

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  3. (1+omega)(1+omega^(2))(1+omega^(5))..........2n factors =

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  4. (1- omega + omega^(2))^(7) + (1 + omega - omega^(2))^(7) =

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

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

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

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

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  9. The value of ((- 1 + isqrt3)/(2))^(100) + ((- 1 - isqrt3)/(2))^(100) i...

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  10. If x = a + b , y = a omega^(2) +b omega and z = a omega + b omega^(2) ...

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  11. If alpha , beta are the imaginary cube roots of unity then alpha^(4) +...

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

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  13. The value of ((-1 + isqrt3)/(2))^(36) + ( (-1 - isqrt3)/(2))^(36) =

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  14. The solution of the equation |z| - z =1 + 2i is

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  15. If (1 + isqrt2)^(x) = 3^(x) , then its only integral solution is

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  16. If barz = iz^(2) then the number of values of z is

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  17. The number of solutions of z + sqrt2 (| z+ 1|) + i=0

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  18. If the complex number z lies on |z| = 1 then (2)/(z) lies on

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  19. If zbarz=4 then the locus of z is

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  20. Match the items of List - I with those of List-II

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