Home
Class 11
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`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If |z|=2, the points representing the complex numbers -1+5z will lie on

If |z|=2, the points representing the complex numbers -1+5z will lie on

For complex number z,|z-1|+|z+1|=2, then z lies on

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

Let z_(1),z_(2) be two complex numbers such that z_(1)+z_(2) and z_(1)z_(2) both are real, then

If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1 , find the locus of z in the complex plane

Let z_1, z_2 be two complex numbers represented by points on the circle |z_1|= and and |z_2|=2 are then

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

Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=pi//2 then

All complex numbers 'z' which satisfy the relation |z-|z+1||=|z+|z-1|| on the complex plane lie on the

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on (a)a l...

    Text Solution

    |

  2. Find all the value of m for which the equation sin^2x-(m-3)sinx+m=0 ...

    Text Solution

    |

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

    Text Solution

    |

  4. If the difference between the roots of the equation x^2+""a x""+""1...

    Text Solution

    |

  5. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

    Text Solution

    |

  6. Find the condition if the roots of a x^2+2b x+c=0 and b x^2-2sqrt(a c ...

    Text Solution

    |

  7. Locus of complex number satisfying "a r g"[(z-5+4i)/(z+3-2i)]=pi/4 is ...

    Text Solution

    |

  8. Solve (x^2-5x+7)^2-(x-2)(x-3)=1.

    Text Solution

    |

  9. If alpha is a complex constant such that alpha z^2+z+ baralpha=0 has...

    Text Solution

    |

  10. Solve the equation x^4-5x^2+4=0.

    Text Solution

    |

  11. The complex number z satisfies z+|z|=2+8i. find the value of |z|-8

    Text Solution

    |

  12. Solve (x^2-2x-3)/(x+1)=0.

    Text Solution

    |

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

    Text Solution

    |

  14. Solve (x^3-4x)sqrt(x^2-1)=0.

    Text Solution

    |

  15. The complex number sinx+icos2x and cosx-isin2x are conjugate to each o...

    Text Solution

    |

  16. Solve (2x-3)/(x-1)+1=(9x-x^2-6)/(x-1)dot

    Text Solution

    |

  17. The points, z1,z2,z3,z4, in the complex plane are the vertices of a pa...

    Text Solution

    |

  18. Using differentiation method check how many roots of the equation x^3-...

    Text Solution

    |

  19. If z=x+iy and w=(1-iz)/(z-i), then |w|=1 implies that in the complex ...

    Text Solution

    |

  20. If the difference between the roots of the equation x^2+""a x""+""1...

    Text Solution

    |