Home
Class 12
MATHS
Let A(z1) and (z2) represent two compl...

Let `A(z_1) and (z_2)` represent two complex numbers on the complex plane. Suppose the complex slope of the line joining A and B is defined as `(z_1-z_2)/(bar z_1-bar z_2)`.If the line `l_1`, with complex slope `omega_1, and l_2`, with complex slope `omeg_2`, on the complex plane are perpendicular then prove that `omega_1+omega_2=0`.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

If z_1 and z_2 are two complex numbers, then the equation of the perpendicular bisector of the segment z_1 and z_2 is

A(z_(1)) and B(z_(2)) are two given points in the complex plane. The locus of a point P(z) in the complex plane satisfying |z-z_(1)|-|z-z_(2)| ='|z1-z2 |, is

If z_(1) and z_(2) are two complex numbers such that z_(1)+2,1-z_(2),1-z, then

Let A, B, C represent the complex numbers z_1, z_2, z_3 respectively on the complex plane. If the circumcentre of the triangle ABC lies at the origin, then the orthocentre is represented by the complex number

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)|+|z_(1)-z_(2)| then

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. if |(1-iz)/(z-i)|=1 prove that the locus of the variable point z in th...

    Text Solution

    |

  2. The equation barbz+bbarz=c, where b is a non-zero complex constant and...

    Text Solution

    |

  3. Let A(z1) and (z2) represent two complex numbers on the complex plan...

    Text Solution

    |

  4. Find the area of the triangle whose vertices in the Argand plane are i...

    Text Solution

    |

  5. Show that the area of the triangle on the Argand diagram formed by the...

    Text Solution

    |

  6. Find the area of the triangle whose vertices represent the three roots...

    Text Solution

    |

  7. The complex numbers z1, z2 and the origin form an equilateral triangle...

    Text Solution

    |

  8. Complex numbers z1 , z2, z3 are the vertices A, B, C respectively of ...

    Text Solution

    |

  9. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

    Text Solution

    |

  10. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

    Text Solution

    |

  11. Complex numbers z1 , z2, z3 are the vertices A, B, C respectively of ...

    Text Solution

    |

  12. The points representing cube roots of unity

    Text Solution

    |

  13. z, w, w^2 are the vertices of an equilateral triangle in the Argand pl...

    Text Solution

    |

  14. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

    Text Solution

    |

  15. If two consecutive vertices of a regular hexagon be z and barz , find ...

    Text Solution

    |

  16. If z1,z2 are two complex numbers representing two consecutive vertices...

    Text Solution

    |

  17. If two vertices of an equilateral triangle are z1,z2 then find the com...

    Text Solution

    |

  18. The equation zbarz+abarz+baraz+b=0, b in R represents circle, if

    Text Solution

    |

  19. Prove that |z-z1|^2+|z-z2|^2 = k will represent a circle if |z1-z2|^2 ...

    Text Solution

    |

  20. Find all circles which are orthogonal to |z|=1and|z-1|=4.

    Text Solution

    |