Home
Class 12
MATHS
The points, z1,z2,z3,z4, in the complex ...

The points, `z_1,z_2,z_3,z_4,` in the complex plane are the vartices of a parallelogram taken in order, if and only if `z_1+z_4=z_2+z_3` `z_1+z_3=z_2+z_4` `z_1+z_2=z_3+z_4` (d) None of these

A

`z_1 +z_14=z_12+z_3`

B

`z_1 +z_13=z_2+z_4`

C

`z_1 +z_2=z_3+z_4`

D

none of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

The points, z_1,z_2,z_3,z_4, in the complex plane are the vartices of a parallelogram taken in order, if and only if (a)z_1+z_4=z_2+z_3 (b)z_1+z_3=z_2+z_4 (c)z_1+z_2=z_3+z_4 (d) None of these

The points z_1, z_2, z_3, z_4 in the complex plane form the vertices of a parallelogram iff :

The point z_(1),z_(2),z_(3),z_(4) in the complex plane are the vertices of a parallogram taken in order, if and only if. (1) z _(1) +z_(4)=z_(2)+z_(3) (2) z_(1)+z_(3) =z_(2) +z_(4) (3) z_(1)+z_(2) =z_(3)+z_(4) (4) z_(1) + z_(3) ne z_(2) +z_(4)

Find the relation if z_(1),z_(2),z_(3),z_(4) are the affixes of the vertices of a parallelogram taken in order.

If z_1,z_2,z_3,z_4 be the vertices of a parallelogram taken in anticlockwise direction and |z_1-z_2|=|z_1-z_4|, then sum_(r=1)^4(-1)^r z_r=0 (b) z_1+z_2-z_3-z_4=0 a r g(z_4-z_2)/(z_3-z_1)=pi/2 (d) None of these

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If z=2+3i, then |z^2|^3 is equal to

    Text Solution

    |

  2. The equation z^5+z^4+z^3+z^2+z+1=0 is satisfied by

    Text Solution

    |

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

    Text Solution

    |

  4. If z^4= (z-1)^4 then the roots are represented in the Argand plane by...

    Text Solution

    |

  5. If |z1 |=|z2|=|z3| = 1 and z1 +z2+z3 =0 then the area of the triangle ...

    Text Solution

    |

  6. In the Argand plane |(z-i)/(z+i)| = 4 represents a

    Text Solution

    |

  7. Suppose z1 + z2 + z3 + z4=0 and |z1| = |z2| = |z3| = |z4|=1. If z1, z2...

    Text Solution

    |

  8. If arg (z-z1)/(z2-z1) = 0 for three distinct complex numbers z,z1,z2 ...

    Text Solution

    |

  9. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

    Text Solution

    |

  10. The locus of the points z satisfying the condition arg ((z-1)/(z+1))=p...

    Text Solution

    |

  11. If a r g((z-2)/(z+2))=pi/4 then the locus of z is

    Text Solution

    |

  12. zbarz+abarz+baraz+b=0 where binR represents a real circle of nonzero r...

    Text Solution

    |

  13. Find the value of sqrt(20+48i)

    Text Solution

    |

  14. If i^p=i^q where i^2=-1 then p-q is divisible by 4.

    Text Solution

    |

  15. If z=(2+3i)/(3+2i), then |z|=

    Text Solution

    |

  16. Find the solutions to the equation (z+i)^2 = 16.

    Text Solution

    |

  17. If z is a nonreal compex number and |z|=1 then z^2+1/z^2=2 .

    Text Solution

    |

  18. State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta)...

    Text Solution

    |

  19. If two nonzero complex numbers z1,z2 be such that z1+z2 is real then t...

    Text Solution

    |

  20. For complex numbersz1=x1+iy1" and " z2=x2+iy2 we write z1 cap z2 if x1...

    Text Solution

    |