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If 1,omega,omega^(2) are the cube roots ...

If `1,omega,omega^(2)` are the cube roots of unity and `alpha=omega+2omega^(2)-3, "then"alpha^(3)+12alpha^(2)+48alpha+3` equals

A

`-63`

B

`-62`

C

`-61`

D

`-60`

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. (1)/(1+2omega)-(1)/(1+omega)+(1)/(2+omega)

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  2. If omega is a complex cube root of unity, then sin[(omega^(10)+omega^(...

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  3. If 1,omega,omega^(2) are the cube roots of unity and alpha=omega+2omeg...

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  4. If alpha, beta are the roots of 1 + x + x^(2)= 0, then the value of al...

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  5. If x^(2) + x + 1 =0 , then the value of (x + (1)/(x))^(2) + (x^(2) + ...

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

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  7. If alpha, beta are the non-real cube roots of 2, then alpha^(6)+beta^...

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  8. If alpha is a non-real root of x^(6)-1=0 then (alpha^(5)+alpha^(3)+alp...

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  9. If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+...

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

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

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  12. 1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...

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

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

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

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

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

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

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

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

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