Home
Class 11
MATHS
If in argand plane the vertices A,B,C of...

If in argand plane the vertices A,B,C of an isoceles triangle are represented by the complex nos `z_1 ,z_2, z_3` respectively where `angleC=90^@` then show that `(z_1-z_2)^2=2(z_1-z_3)(z_3-z_2)`

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

The vertices A,B,C of an isosceles right angled triangle with right angle at C are represented by the complex numbers z_(1) z_(2) and z_(3) respectively. Show that (z_(1)-z_(2))^(2)=2(z_(1)-z_(3))(z_(3)-z_(2)) .

In the complex plane, the vertices of an equlitateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that, (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

If the vertices of an equilateral triangle be represented by the complex numbers z_(1),z_(2),z_(3) on the Argand diagram, then prove that, z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

If the vertices of an equilateral traingle be represented by the complex numbers z_1 , z_2 , z_3 , then prove that z_1^2+z_2^2+z_3^2=3z_0^2 and z_0 be the circumcenter of the triangle.

An equilateral triangle in the Argan plane has vertix as z_1 , z_2 and z_3 which are there complex no show that 1/(z_1-z_2)+1/(z_3-z_1)+1/(z_2-z_3)=0

If z_1,z_2,z_3 represent three vertices of an equilateral triangle in argand plane then show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled triangle with right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

On the Argand plane z_1, z_2a n dz_3 are respectively, the vertices of an isosceles triangle A B C with A C=B C and equal angles are thetadot If z_4 is the incenter of the triangle, then prove that (z_2-z_1)(z_3-z_1)=(1+sectheta)(z_4-z_1)^2dot

if z_1, z_2, z_3 are the vertices pf an equilateral triangle inscribed in the circle absz=1 and z_1=i , then

In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a complex number) represent vertices of

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. Find the real values of x and y for which the following equation is sa...

    Text Solution

    |

  2. Let the complex numbers z1,z2 and z3 be the vertices of an equilateral...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |