Home
Class 12
MATHS
The complex numbers z(1) , z(2) and z(3)...

The complex numbers `z_(1) , z_(2)` and `z_(3)` satisfying `(z_(1) - z_(3))/(z_(2) - z_(3)) = (1 - isqrt3)/(2)` are the vertices of a triangle which is

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

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise EXERCISE - I|49 Videos

  • CIRCLES

    AAKASH SERIES|Exercise PRACTICE EXERCISE|164 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

Similar Questions

Explore conceptually related problems

If z_1,z_2,z_3 are the vertices of a triangle then its centroid is

The complex number z satisfying z^(2) + |z| = 0 is

If z^(1) =2 -I, z_(2)=1+i , find |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

If z_(1) , z_(2) are two complex numbers satisfying |(z_(1) - 3z_(2))/(3 - z_(1) barz_(2))| = 1 , |z_(1)| ne 3 then |z_(2)|=

If z_(1)=1-2i, z_(2)=1+i and z_(3) =3+4i," then "((1)/(z_(1))+(3)/(z_(2)))(z_(3))/(z_(2))=

If z_(1)=(2,-1),z_(2)=(6,3) find z_(1)-z_(2)

For any two complex numbers z_(1) and z_(2) , prove that Re ( z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)

If z_(1)=(3,5) and z_(2)=(2,6) find, z_(1).z_(2)

For all complex numbers z_(1) , z_(1) satisfying |z_(1)| = 12 and |z_(2) - 3 - 4i| = 5 , the minimum value of |z_(1) - z_(2)| is

AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. In Argand diagram , O , P , Q represent the origin , z and z +iz resp...

    Text Solution

    |

  2. If a is a complex number and b is a real number then the equation bar...

    Text Solution

    |

  3. The complex numbers z(1) , z(2) and z(3) satisfying (z(1) - z(3))/(z(2...

    Text Solution

    |

  4. The cube roots of unity in an Argand plane represent the vertices of a...

    Text Solution

    |

  5. Let z(1) and z(2) be two non-zero complex numbers such that (z(1))/(z(...

    Text Solution

    |

  6. Let the complex number z(1) , z(2) , z(3) be the vertices of an equila...

    Text Solution

    |

  7. Log (log i) =

    Text Solution

    |

  8. The value of i^(i^(-i…..oo)) = x + iy then x^(2) + y^(2) =

    Text Solution

    |

  9. The real and imaginary parts of log (1 + i) =

    Text Solution

    |

  10. (sin (log i^(i)))^3 + (cos (log i^(i)))^3 =

    Text Solution

    |

  11. z = 6. e^(i (pi)/(3)) then |e^(iz)| =

    Text Solution

    |

  12. tan{ilog((a-ib)/(a+ib))}=

    Text Solution

    |

  13. The locus represented by |z-1|=|z+i| is

    Text Solution

    |

  14. Let z = 1 - t + isqrt(t^(2) + t + 2) , where t is a real parameter . T...

    Text Solution

    |

  15. In the Argand Diagram , all the complex numbers z satisfying |z - 4i| ...

    Text Solution

    |

  16. The region of the argand plane defined by |z-i| + |z +i| le 4 is

    Text Solution

    |

  17. If (z+2)/(z+6i) is purely real then the locus of z = x +iy is

    Text Solution

    |

  18. If |z -1| lt 2 |z - 2| then the locus of z = x + iy is

    Text Solution

    |

  19. If the imaginary part of (2z + 1)/(iz+ 1) is -2 , then the locus of th...

    Text Solution

    |

  20. z = x + iy and w = (1 - iz)/(z-i) , then |w| = 1 implies in the comple...

    Text Solution

    |