Home
Class 11
MATHS
let z1=10+6i and z2=4+6i if z is nay com...

let `z_1=10+6i` and `z_2=4+6i` if z is nay complex number such that argument of `(z-z_1)/(z-z_2)` is `pi/4` the prove that `abs(z-7-9i)=3sqrt2`

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

If z=-i-1 is a complex number,then arg (z) will be

Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then prove that |z|=1.

If z be any complex number such that abs(3z-2)+abs(3z+2)=4 then locus of z is

Solve : |z|+z=2+i (z being a complex number)

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

z is a complex number. The minimum value of |z | + I z - 2| is

if z_1 and z_2 are two complex numbers such that absz_1lt1ltabsz_2 then prove that abs(1-z_1barz_2)/abs(z_1-z_2)lt1

If z_1 and z_2 be two complex numbers such that abszle1, absz_2le1, abs(z_1+iz_2)=abs(z_1-iz_2)=2 , then z_1 equals

If z_1 and z_2 be two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2| ,then prove that argz_1-argz_2=0 .

If z_(1)and z_(2) be any two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then prove that, arg z_(1)=arg z_(2) .

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. Let the complex numbers z1,z2 and z3 be the vertices of an equilateral...

    Text Solution

    |

  2. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

    Text Solution

    |

  3. let z1=10+6i and z2=4+6i if z is nay complex number such that argument...

    Text Solution

    |

  4. if iz^3+z^2-z+i=0 then show that absz=1

    Text Solution

    |

  5. let z1 and z2 be roots of the equation z^2+pz+q=0 where the coefficien...

    Text Solution

    |

  6. For complex numbers z and w prove that absz^2w-abs(w)^2z=z-w if and on...

    Text Solution

    |

  7. if z1 and z2 are two complex numbers such that absz1lt1ltabsz2 then p...

    Text Solution

    |

  8. find the centre and radius of the circle formed by all the points repr...

    Text Solution

    |

  9. Let omega ne1 be a complex cube root of unity if (3-3omega+2omega^2)^(...

    Text Solution

    |

  10. For any integer k let alphak=cos((kpi)/7)+isin((kpi)/7) where i=sqrt(-...

    Text Solution

    |

  11. A complex number z is said to be unimodular if absz=1 suppose z1 and z...

    Text Solution

    |

  12. The value of ((1+sqrt3i)/(1-sqrt3i))^64+((1-sqrt3i)/(1+sqrt3i))^64

    Text Solution

    |

  13. Find the maximum value of absz when abs(z-3/z)=2 ,z being a complex nu...

    Text Solution

    |

  14. If z is a complex number such that abszge2 then the minimum value of a...

    Text Solution

    |

  15. Let z1,z2 be two fixed complex numbers in the Argand plane and z be an...

    Text Solution

    |

  16. In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a comple...

    Text Solution

    |

  17. Suppose that z1, z2, z3 are three vertices of an equilateral triangle ...

    Text Solution

    |

  18. The value of absz^2+abs(z-3)^2+abs(z-i)^2 is minimum when z equals

    Text Solution

    |

  19. Let z1 be a fixed point on the circle of radius 1 centered at the orig...

    Text Solution

    |

  20. Let alpha ,beta denote the cube roots of unity other than 1 and alpha ...

    Text Solution

    |