Home
Class 12
MATHS
If z(1),z(2),z(3),…………..,z(n) are n nth ...

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

A

`|z_(k)|=k|z_(n)+1|`

B

`|z_(k+1)|=k|z_(k)|`

C

`|Z_(K+1)|=|Z_(k)|Z_(k+1)|`

D

`|z_(k)|=|z_(k+1)|`

Text Solution

Verified by Experts

The correct Answer is:
d
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|15 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 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 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

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),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

If z_(1),z_(2),z_(3),z_(4), are the non-real complex fifth roots of unity,then the sum of coefficient in the expansion of (3+z_(1)x+z_(2)x^(2)+z_(3)x^(3)+z_(4)x^(4))^(5) is

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

If z_(1),z_(2),z_(3)………….z_(n) are in G.P with first term as unity such that z_(1)+z_(2)+z_(3)+…+z_(n)=0 . Now if z_(1),z_(2),z_(3)……..z_(n) represents the vertices of n -polygon, then the distance between incentre and circumcentre of the polygon is

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

If z_1,z_2,z_3,………..z_(n-1) are the roots of the equation 1+z+z^2+…….+z^(n-1)=0, where n epsilon N, ngt2 then (A) z_1,z_2, …z_(n-1) are terms of a G.P. (B) z_1,z_2,……,z_(n-1) are terms of an A.P. (C) |z_1|=|z_2|=|z_3|=.|z_(n-1)|!=1 (D) none of these

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...

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. If z1, z2, z3, z4 are the affixes of four point in the Argand plane, z...

    Text Solution

    |

  2. The value of sum(r=1)^(8)(sin(2rpi)/9+icos(2rpi)/9), is

    Text Solution

    |

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

    Text Solution

    |

  4. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers then arg...

    Text Solution

    |

  5. If |z(1)|=|z(2)| and arg (z(1))+"arg"(z(2))=0, then

    Text Solution

    |

  6. If one vertex of a square whose diagonals intersect at the origin is 3...

    Text Solution

    |

  7. The value of z satisfying the equation logz+logz^(2)+……..+logz^(n)=0...

    Text Solution

    |

  8. If |z(1)|=|z(2)|=………….=|z-(n)|=1, then the value of |z(1)+z(2)+………+z(n...

    Text Solution

    |

  9. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

    Text Solution

    |

  10. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

    Text Solution

    |

  11. Let z and omega be two non-zero complex numbers, such that |z|=|omega|...

    Text Solution

    |

  12. If z ne 0 be a complex number and "arg"(z)=pi//4, then

    Text Solution

    |

  13. (1+i)^8+(1-i)^8=?

    Text Solution

    |

  14. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

    Text Solution

    |

  15. If alphaand betaare different complex numbers with |beta|=1,then fin...

    Text Solution

    |

  16. For any complex number z, the minimum value of |z|+|z-1|

    Text Solution

    |

  17. If (3pi)/(2) gt alpha gt 2 pi, find the modulus and argument of (1 -...

    Text Solution

    |

  18. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Argand plane, then...

    Text Solution

    |

  19. Area of the triangle formed by 3 complex numbers, 1+i,i-1,2i, in the A...

    Text Solution

    |

  20. If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6...

    Text Solution

    |