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The common roots of the equation `z^3+2z^2+2z+1=0&z^(1985)+z^(100)+1=0` are: `1,omega` b. `1,omega^2` c. `omega,omega^2` d. none of these

A

`omega , omega^(2)`

B

`1, omega, omega^(2)`

C

`- 1, omega, omega^(2)`

D

`- omega, - omega^(2)`

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A
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ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
  1. If t^(2) + t + 1 = 0 then, the value of ( t + (1)/( t))^(2) + ( t^(...

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  2. If z^(2) + z + 1 = 0 where z is a complex number then the value of ...

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  3. The common roots of the equation z^3+2z^2+2z+1=0&z^(1985)+z^(100)+1...

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  4. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

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  5. (( - 1 + sqrt""(-3))/(2))^(100) + ((- 1 - sqrt""(-3))/( 2))^(100) equ...

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  6. ( i + sqrt(3) )^(100) + (i - sqrt(3))^(100) + 2 ^(100) =

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  7. What is the value of : ((-1+isqrt(3))/(2))^(3n) + (( -1-isqrt(3))/(2...

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  8. If i=sqrt(-1), then 4+5(-1/2+(isqrt(3))/(2))^(334)+3(1/2+(isqrt(3))/...

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  9. If 1;w;w^2 are cube root of unity and n is a positive integer;then 1+w...

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  10. If n is a multiple of 3, then 1 + omega ^(n) + omega ^(2n) =

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  11. If alpha , beta are the roots of x^(2) - 2 x + 4 = 0 " then " (alph...

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  12. If g(x) and h(x) are two polynomials such that the polynomials P(x)=g(...

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  13. If alpha , beta are complex cube roots of unity and x = a + b, y = ...

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  14. If a+b+c=0 and omega,omega^2 are imaginary cube roots of unity, then (...

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  15. If omega is a cube root of unity but not equal to 1, then minimum valu...

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  16. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

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  17. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

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  18. If omega pm 1 is a cube root of unity, the value of (a + b omega + c o...

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  19. If alpha, beta, gamma are the cube roots of p, p lt 0 then for an...

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  20. If alpha , beta , gamma are cube roots of p lt 0, then for any x , y,...

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