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

A

`(n3^(n-1))/(3^(n) -1)+(1)/(2)`

B

`(n3^(n-1))/(3^(n)-1)+1`

C

`(n3^(n-1))/(3^(n)-1)-1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|22 Videos
  • COMPLEX NUMBER

    FIITJEE|Exercise COMPREHENSION - I|3 Videos
  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|10 Videos
  • CIRCLE

    FIITJEE|Exercise Numerical Based|2 Videos
  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 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 :

FIITJEE-COMPLEX NUMBER-ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I
  1. A complex number z with (Im)(z)=4 and a positive integer n be such tha...

    Text Solution

    |

  2. For complex number z, the minimum value of |z| + |Z- cos alpha-I sin a...

    Text Solution

    |

  3. Equation of tangent drawn to circle abs(z)=r at the point A(z(0)), is

    Text Solution

    |

  4. Delta ABC be a triangle inscribed in a circle |z|=1 when B(Z1), C(Z2) ...

    Text Solution

    |

  5. If tangent at Z1, Z2 on the circle |Z- Z0|=r intersect at Z3. Then((Z3...

    Text Solution

    |

  6. If |(z-z1)/(z-z2)|=1, where z1 and z2 are fixed complex numbers and z ...

    Text Solution

    |

  7. Let arg(z(k))=((2k+1)pi)/(n) where k=1,2,………n. If arg(z(1),z(2),z(3),…...

    Text Solution

    |

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

    Text Solution

    |

  9. For positive integer n1,n2 the value of the expression (1+i)^(n1) +(1+...

    Text Solution

    |

  10. If z1 , z2, z3 are complex numbers such that |z1|= |z2| = |z3|= |(1)/(...

    Text Solution

    |

  11. If |z+(2)/(z)|=2 then the maximum value of |z| is

    Text Solution

    |

  12. If . ( tan theta + (sin. (theta)/(2) +cos. (theta)/(2)))/(1+2i sin. (t...

    Text Solution

    |

  13. If a, b in C and z is a non zero complex number then the root of the e...

    Text Solution

    |

  14. If the ratio (1-z)/(1+z) is purely imaginary, then

    Text Solution

    |

  15. If z1 and z2 are two distinct non-zero complex number such that |z1|= ...

    Text Solution

    |

  16. If |z1|=1, |z2| = 2, |z3|=3 and |9z1 z2 + 4z1 z3+ z2 z3|=12, then the ...

    Text Solution

    |

  17. If z1, z2 and z3 be the vertices of Delta ABC, taken in anti-clock wi...

    Text Solution

    |

  18. If the point A1, A2,….,A8 be the affixes of the roots of the equation...

    Text Solution

    |

  19. Statement - 1 : If for any complex number z, |z-2|+|z-3|=4, then are ...

    Text Solution

    |

  20. Statement - 1: consider an ellipse with foci at A(z1) and B(z2) in the...

    Text Solution

    |