Home
Class 12
MATHS
If z(1),z(2),z(3),z(4) are the affixes ...

If `z_(1),z_(2),z_(3),z_(4)` are the affixes of the four points in the Argand plants , z is the affix of a point such that `|z-z_(1)|=|z-z_(2)|= |z-z_(3)| = |z-z_(4)|`, then prove that `z_(1),z_(2),z_(3),z_(4)` are concycline.

A

concylic

B

vertices of a triangle

C

vertices of a rhombus

D

in a straight line

Text Solution

Verified by Experts

The correct Answer is:
a
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • COMPLEX NUMBERS

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

  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|53 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

Similar Questions

Explore conceptually related problems

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then prove that z_1, z_2, z_3, z_4 are concyclic.

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = |z_(1)-z_(2)|

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| - |z-z_(2)|= |z_(1)-z_(2)|

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers z_(1),z_(2),z_(3),z_(4) are concyclic.

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| = |z-z_(2)|

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|-|z-z_(2)|= constant (ne |z_(1)-z_(2)|)

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = constant ne (|z_(1)-z_(2)|)

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|= k|z-z_(2)|, k in R^(+), k ne 1

If z_(1),z_(2)andz_(3) are the affixes of the vertices of a triangle having its circumcentre at the origin. If zis the affix of its orthocentre, prove that Z_(1)+Z_(2)+Z_(3)-Z=0.

OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
  1. If the complex number z(1) " and " z(2) are such that arg (z(1)) - ar...

    Text Solution

    |

  2. The join of z(1)=a+ib and z(2)=1/(-a+ib) passes through

    Text Solution

    |

  3. If z(1),z(2),z(3),z(4) are the affixes of the four points in the Ar...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If z(1),z(2) and z(3), z(4) are two pairs of conjugate complex numbers...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. The value of z satisfying the equation logz+logz^2+dot+logz^n=0i s

    Text Solution

    |

  10. If |z(1)|= |z(2)|= ….= |z(n)|=1, prove that |z(1) + z(2) + …+ z(n)|= |...

    Text Solution

    |

  11. If omega is a cube root of unity and (1+omega)^7=A+Bomega then find th...

    Text Solution

    |

  12. If omega(!=1) is a cube root of unity, then value of the determinant|1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. (1+i)^8+(1-i)^8=?

    Text Solution

    |

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

    Text Solution

    |

  17. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...

    Text Solution

    |