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If 1,alpha,alpha^(2),……….,alpha^(n-1) ar...

If `1,alpha,alpha^(2),……….,alpha^(n-1)` are `n^(th)` root of unity, the value of `(3-alpha)(3-alpha^(2))(3-alpha^(3))……(3-alpha^(n-1))`, is

A

n

B

0

C

`(3^(n)- 1)/( 2)`

D

`(3 ^(n) + 1)/( 2)`

Text Solution

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The correct Answer is:
C
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ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
  1. If If 1, alpha(1), alpha(2), alpha(3) , . . . alpha(n - 1) are the n...

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  2. If beta ne 1 be any nth root of unity, then 1 + 3 beta + 5 beta ^...

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  3. If 1,alpha,alpha^(2),……….,alpha^(n-1) are n^(th) root of unity, the va...

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  4. If p is a multiple of n , then the sum of pth powers of nth roots of u...

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  5. If p is not a multiple of n, then the sum of pth powers of nth root...

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  6. If alpha (1), alpha(2), . . . alpha (100) are all the 100 th roots of...

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  7. If z = ( sqrt(3) + i)/( 2) then ( z^(101) + i ^(103))^(105) equals

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  8. The square root of 3+4i is

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  9. The square root of the number 5 + 12 i is

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  10. The square root of the numbers (- 7 - 24i) is

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  11. (sqrt(5 + 12 i ) + sqrt( 5 - 12 i) ) /(sqrt(5 + 12 i ) - sqrt( 5 - 12 ...

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  12. If ( sqrt(3) + i) ^(100) = 2^(99) (a + ib) , " then " a^(2) + b^(2) i...

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  13. If ( sqrt(3) + i) ^(100) = 2 ^(99) (a + i b) then b =

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  14. If ( sqrt( 3) + i) ^(10) = a + ib then, a and b are respectively

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  15. The solution of the equation (1 + i sqrt(3))^(x) = 2^(x) are in

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  16. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

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  17. Sum of sixth power of the roots of the equation t^(2) - 2t + 4 = 0 i...

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  18. (1 + i) ^(8) + (1 - i) ^(8) =

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  19. If [ (sqrt(3) // 2 + (1 //2)i)/(sqrt(3) // 2 - (1//2)i)] ^(120) = a +...

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  20. (-64)^(1//4) is equal to-

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