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The product of all n^(th) root of unity...

The product of all `n^(th)` root of unity is always

A

1

B

`-1`

C

`(- 1)^(n - 1)`

D

`(-1)^(n)`

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 alpha is an n th root of unity other than unity itself, then the ...

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  2. If omega is an imaginary fifth root of unity, then find the value of l...

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  3. The product of all n^(th) root of unity is always

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  4. The roots of the cubic equation (z + ab)^(3) = a ^(3) , a ne 0 represe...

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  5. If If 1, alpha(1), alpha(2), alpha(3) , . . . alpha(n - 1) are the n...

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

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

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

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

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

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

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  12. The square root of 3+4i is

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

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

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

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

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

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

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

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

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