Home
Class 12
MATHS
The complex numbers z1, z2 and z3 satisf...

The complex numbers `z_1, z_2 and z_3` satisfying `(z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2` are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

A

of area zero

B

right angled isosceles

C

equilateral

D

obtuse angled isosceles

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

The complex numbers z_(1),z_(2),z_(3) stisfying (z_(2)-z_(3))=(1+i)(z_(1)-z_(3)).where i=sqrt(-1), are vertices of a triangle which is

The complex numbers z 1 ​ ,z 2 ​ and z 3 ​ satisfying z 2 ​ −z 3 ​ z 1 ​ −z 3 ​ ​ = 2 1− 3 ​ i ​ are the vertices of a triangle which is

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

The complex numbers z_1=1+2i,z_2=4-2i and z_3=1-6i form the vertices of a (A) a right angled triangle (B) isosceles triangle (C) equilateral triangle (D) triangle whose one of the sides is of length 8

For any complex numbers z_1,z_2 and z_3, z_3 Im(bar(z_2)z_3) +z_2Im(bar(z_3)z_1) + z_1 Im(bar(z_1)z_2) is

If z_(1)=1+2i, z_(2)=2+3i, z_(3)=3+4i , then z_(1),z_(2) and z_(3) represent the vertices of a/an.

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 , find the minimum value of |z_1-z_2|

If the complex numbers z_(1), z_(2), z_(3) represent the vertices of an equilateral triangle, and |z_(1)|= |z_(2)| = |z_(3)| , prove that z_(1)+ z_(2) + z_(3)=0

Let z_1 , z _2 and z_3 be three complex numbers such that z_1 + z_2+ z_3 = z_1z_2 + z_2z_3 + z_1 z_3 = z_1 z_2z_3 = 1 . Then the area of triangle formed by points A(z_1 ), B(z_2) and C(z_3) in complex plane is _______.

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. The shaded region ,where P=(-1 ,0)Q=(-1 + sqrt(2),sqrt(2)) R=(-1+sq...

    Text Solution

    |

  2. Let 0ltalphalt(pi)/(2) be a fixed angle. If P=(costheta,sintheta)andQ=...

    Text Solution

    |

  3. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. Let z=costheta+isin theta, where i=sqrt(-1). Then the value of sum(m=1...

    Text Solution

    |

  6. If omega is a cube root of unity but not equal to 1, then minimum valu...

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. about to only mathematics

    Text Solution

    |

  9. Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1), and r, s in {1, 2, 3}. Let ...

    Text Solution

    |

  10. Let a,b in R and a^(2)+b^(2) ne 0. Suppose S={z in C:z=(1)/(a+ibt),t...

    Text Solution

    |

  11. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  12. The quadratic equation p(x)=0 with real coefficients has purely imagin...

    Text Solution

    |

  13. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

    Text Solution

    |

  14. Let a,b,x and y be real numbers such that a-b =1 and y ne 0. If the ...

    Text Solution

    |

  15. If z(1)=p+iq and z(2) = u = iv are complex numbers such that |z(1)|=...

    Text Solution

    |

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

    Text Solution

    |

  17. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. Find the centre and radius of the circle formed by all the points repr...

    Text Solution

    |

  20. If one of the vertices of the square circumscribing the circle abs(z-1...

    Text Solution

    |