Home
Class 12
MATHS
If P(z(1)),Q(z(2)),R(z(3)) " and " S(z(4...

If `P(z_(1)),Q(z_(2)),R(z_(3)) " and " S(z_(4))` are four complex numbers representing the vertices of a rhombus taken in order on the complex plane, which one of the following is held good?

A

`z_(1)+z_(3)=z_(2)+z_(4)`

B

`|z_(1)-z_(2)|=|z_(2)-z_(3)|`

C

`(z_(1)-z_(3))/(z_(2)-z_(4))` is purely imaginary

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICS TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION-I)|3 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION-II)|3 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSERTION - REASONING|8 Videos

  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos

  • MATRICES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

P(z_(1)),Q(z_(2)),R(z_(3)) and S(z_(4)) are four complex numbers representing the vertices of a rhombus taken in order on the comple plane, then which one of the following is/are correct?

P(z_1),Q(z_2),R(z_3)a n dS(z_4) are four complex numbers representing the vertices of a rhombus taken in order on the complex lane, then which one of the following is/ are correct? (z_1-z_4)/(z_2-z_3) is purely real a m p(z_1-z_4)/(z_2-z_3)=a m p(z_2-z_4)/(z_3-z_4) (z_1-z_3)/(z_2-z_4) is purely imaginary It is not necessary that |z_1-z_3|!=|z_2-z_4|

If z_(1),z_(2),z_(3),z_(4), represent the vertices of a rhombus taken in anticlockwise order,then

If z_(1) , z_(2), z_(3) are three complex numbers in A.P., then they lie on :

If z_(1),z_(2),z_(3),z_(4) are the vertices of a square in that order,then which of the follawirg do(es) rot hold good?

The complex number z_(1)z_(2)z_(3) are the vertices of a triangle.Then the complex number z which make the triangle into parallelogram is

FIITJEE-MATHEMATICS TIPS-MCQ (MULTIPLE CORRECT)
  1. If alpha is a root of the equation 2x(2x+1)=1, then the other root is

    Text Solution

    |

  2. Let vec(a)=2hati-hatj+hatk,vec(b)=hati+2hatj-hatk and vec( c )=hati+ha...

    Text Solution

    |

  3. If P(z(1)),Q(z(2)),R(z(3)) " and " S(z(4)) are four complex numbers re...

    Text Solution

    |

  4. The largest coefficient in the expansion of (4+3x)^(25) is

    Text Solution

    |

  5. Given that the 4th term in the expansion of [2+(3//8x)]^(10) has the m...

    Text Solution

    |

  6. If Deltar=|[2^(r-1),1/(r(r+1)),sin rtheta],[x, y, z],[2^n-1, n/(n+1),(...

    Text Solution

    |

  7. If a, b, c are even natural numbers, then Delta=|{:(a-1,a,a+1),(b-1,b,...

    Text Solution

    |

  8. There are n locks and n matching keys. If all the locks and keys are t...

    Text Solution

    |

  9. The number of ways in which we can choose 2 distinct integers from 1 t...

    Text Solution

    |

  10. Let n be a positive integer with f(n) = 1! + 2! + 3!+.........+n! and ...

    Text Solution

    |

  11. If m and n are positive integers more than or equal to 2, mgtn, then (...

    Text Solution

    |

  12. A drawer contains red and black balls. When two balls are drawn at ran...

    Text Solution

    |

  13. If A, B, C and D are four points with position vectors 3hati, 3hatj, 3...

    Text Solution

    |

  14. If |(a,b,aalpha+b),(b,c,balpha+c),(a alpha+b,b alpha+c,0)|=0 then

    Text Solution

    |

  15. The equation x^3/4((log)2x)^(2+(log)2x-5/4)=sqrt(2) has (1989, 2M) at ...

    Text Solution

    |

  16. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

    Text Solution

    |

  17. The nature of the intersection of the set of planes: 2x-4y+2z=5,5x-y...

    Text Solution

    |

  18. Let PM be the perpendicualr from the point P(1, 2, 3) to x-y plane. If...

    Text Solution

    |

  19. The det Delta=|{:(d^2+r,de,df),(de,e^2+r,ef),(df,ef,f^2+r):}| is divis...

    Text Solution

    |

  20. The inverse of a skew symmetric matrix is

    Text Solution

    |