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If 1,alpha1,alpha2,…..alpha(n-1) are the...

If `1,alpha_1,alpha_2,…..alpha_(n-1)` are the `n^(th)` roots of unity and n is an odd natural number then
`(1+alpha_1)(1+alpha_2)…..(1+alpha_(n-1))=`

A

1

B

`-1`

C

0

D

none

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+...

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  2. If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity then (1...

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  3. If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity and n i...

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  4. 1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...

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  5. If 1,z1z2,……z(n-1) are the n^th roots of unity, then (1-z1)(1-z2)…..(1...

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  6. If alpha is an n^(th) root of unity then prove that 1+2alpha+3alpha^2+...

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

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  8. Statement-I : If xn=cos(pi//2^n)+isin (pi//2^n) then x1.x2.x3…..=-...

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  9. If X(n)="cos"(pi)/(2^(n))+"isin"(pi)/(2^(n)), then x(1), x(2), x(3)......

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  10. If x(n)=cos((pi)/(4^(n)))+i sin ((pi)/(4^(n))), then x(1), x(2), x(3)....

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  11. sum(k=1)^6[sin((2kpi)/(7))-icos((2kpi)/(7))]=

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  12. If z(k)=cos((kpi)/(10))+isin((kpi)/(10)), then z(1)z(2)z(3)z(4) is equ...

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  13. The cube roots of 1+I are

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  14. The values of (1-sqrt3i)^(1//3) are

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  15. Find all the values of (sqrt3 + i) ^(1/4) .

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  16. The product of the four values of (1/2+i(sqrt3)/(2))^(3//4) is

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  17. The product of the values of [cos""(pi)/(3)+isin""(pi)/(3)]^(3//4) is

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  18. The product of the distinct (2n)^(th) roots 1+isqrt3 is

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  19. If x^6+1=0, then x =

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  20. The number of common roots of 15th and of 25th roots of unity are

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