Home
Class 12
MATHS
If ,Z1,Z2,Z3,........Z(n-1) are n^(th) ...

If `,Z_1,Z_2,Z_3,........Z_(n-1)` are `n^(th)` roots of unity then the value of `1/(3-Z_1)+1/(3-Z_2)+..........+1/(3-Z_(n-1))` is equal to

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

1,z_(1),z_(2),z_(3),......,z_(n-1), are the nth roots of unity, then (1-z_(1))(1-z_(2))...(1-z_(n-1)) is

If z_(0), z_(1),z_(2),...,z_(5) be 6^(th) roots of unity where z_(0)=1 then the value of (1)/(3)(2+z_(1))(2+z_(2))...(2+z_(5)) is...

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

Let 1, z_(1),z_(2),z_(3),…., z_(n-1) be the nth roots of unity. Then prove that (1-z_(1))(1 - z_(2)) …. (1-z_(n-1))= n . Also,deduce that sin .(pi)/(n) sin.(2pi)/(pi)sin.(3pi)/(n)...sin.((n-1)pi)/(n) = (pi)/(2^(n-1))

If z_(1) and z_(2) are two n^(th) roots of unity, then arg (z_(1)/z_(2)) is a multiple of

If z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

If 1,z_(1),z_(2),z_(3).....z_(n-1) be n^(th) roots if unity and w be a non real complex cube root of unity, then prod_(r=1)^(n-1)(w-z_(r)) can be equal to

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

If 1,z_(1),z_(2),z_(3),......,z_(n-1) be the n, nth roots of unity and omega be a non-real complex cube root of unity,then prod_(r=1)^(n-1)(omega-z_(r)) can be equal to

If the fourth roots of unity are z_(1),z_(2),z_(3),z_(4) and z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(4)^(2) is equal to :

RESONANCE DPP-JEE MAINS-All Questions
  1. Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4))) and g be the inverse of f then...

    Text Solution

    |

  2. Evaluate the determinants |[3,-1,-2],[0,0,-1],[3,-5,0]|

    Text Solution

    |

  3. If ,Z1,Z2,Z3,........Z(n-1) are n^(th) roots of unity then the value ...

    Text Solution

    |

  4. Evaluate the determinants |[3,-1,-2],[0,0,-1],[3,-5,0]|

    Text Solution

    |

  5. The probability that the graph of y=16x^2 +8(a +5)x-7a-5=0, is strictl...

    Text Solution

    |

  6. Evaluate the determinants in |2 4-5-1|

    Text Solution

    |

  7. The number of values of k, for which the system of equations (k""+"...

    Text Solution

    |

  8. In a city no two persons have identical set of teeth and there is n...

    Text Solution

    |

  9. Solve: ((x-1)(x-2)(x-3))/((x+1)(x+2)(x+3))>1

    Text Solution

    |

  10. Let f(x ,y)=x y^2 if xa n dy satisfy x^2+y^2=9 then the minimum value ...

    Text Solution

    |

  11. Solve: (x-1)/x-(x+1)/(x-1)<2

    Text Solution

    |

  12. If a, b, c are distinct odd integers and omega is non real cube root o...

    Text Solution

    |

  13. If f(x)=x^4-2x^3+3x^2-a x+b is a polynomial such that when it is divi...

    Text Solution

    |

  14. The range of the function, f(x)= (1+sec^-1x) (1 + cos^-1 x) is

    Text Solution

    |

  15. The expression [root(3)root(6)(a^9) ]^4[root(6)root(3)(a^9)]^4 is sim...

    Text Solution

    |

  16. The real value of k for which the sysmtem of equation 2k x-2y+3z=0, x+...

    Text Solution

    |

  17. In the figure, if A B=A C ,/B A D=30^0 and A E=A D , then x is equal t...

    Text Solution

    |

  18. The number of value(s) of x satisfying 1-log9(x+1)^2=1/2log(sqrt(3))((...

    Text Solution

    |

  19. If x=3-sqrt(8),t h e nx^3+1/(x^3) is equal to 6 b. 198 c. 6sqrt(2) d. ...

    Text Solution

    |

  20. If f(x)=x^(3)+3x^(2)+4x+asinx+bcosx, forall x in R is a one-one fuctio...

    Text Solution

    |