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

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

A

42

B

48

C

52

D

64

Text Solution

Verified by Experts

The correct Answer is:
D
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(3+5omega+3omega^(2))^(6)

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) =

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

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 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 . (a+ b)^(3) + ( a omega + b omega ^(2))^(3) + ( a omega^(2) + b omega)^(3)

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)

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 prove that (1 - omega + omega^(2))^(6) + ( 1 - omega ^(2) + omega)^(6) = 128 = (1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7)

If 1 , omega , omega^(2) are the cube roots of unity, then prove that ( x + y + z) ( x + y omega + z omega^(2)) ( x + yomega^(2) + z omega) = x^(3) + y^(3) + z^(3) - 3xyz

AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. The value of sqrt(x^(2) + 2ix- 1) is

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  2. If n is an integer and not a multiple of 3 then omega^(n) + omega^(2n...

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

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

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  5. (1- omega + omega^(2))^(7) + (1 + omega - omega^(2))^(7) =

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  6. (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-om...

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

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

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

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

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

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

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

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

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

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

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

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

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

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