Home
Class 12
MATHS
The vertices of a square are z1,z2,z3 an...

The vertices of a square are `z_1,z_2,z_3 and z_4` taken in the anticlockwise order, then `z_3=`

A

`z_(1)+z_(2)+z_(3)+z_(4)=0`

B

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

C

`"amp"((z_(2)-z_(4))/(z_(1)-z_(3)))=pi/2`

D

`"amp"(z_(1)-z_(2))/(z_(3)-z_(4))=pi/2`

Text Solution

Verified by Experts

The correct Answer is:
c
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Exercise|131 Videos
  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

Similar Questions

Explore conceptually related problems

Statement -1 : if 1-i,1+i, z_(1) and z_(2) are the vertices of a square taken in order in the anti-clockwise sense then z_(1) " is " i-1 and Statement -2 : If the vertices are z_(1),z_(2),z_(3),z_(4) taken in order in the anti-clockwise sense,then z_(3) =iz_(1) + (1+i)z_(2)

z_1,z_2 are represented by two consecutive vertices of a rhombus, the angle at z_1 being pi/4 . Find the complex numbers z_3,z_4 represented by the other vertices, the vertices z_1,z_2,z_3,z_4 being in the anticlockwise sense and origin being the center.

If z_(1),z_(2),z_(3) be vertices of an equilateral triangle occurig in the anticlockwise sense, then

If A(2+3i) and B(3+4i) are two vertices of a square ABCD (taken in anticlockwise order)in a complex plane, then the value of |Z_(3)|^(2)-|Z_(4)|^(2) (Where C is Z_(3) and D is Z_(4) ) is equal to

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

Let z_(1),z_(2),z_(3),z_(4) be the vertices A,B,C,D respectively of a square on the Argand diagramtaken in anticlockwise direction then prove that: 2z_(2)=(1+i)z_(1)+(1-i)z_(3)

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

If two vertices of an equilateral triangle are z_1,z_2 then find the complex number z_3 represented by the third vertex where z_1 , z_2,z_3 are anticlockwise.

z_(1),z_(2),z_(3) are the vertices of an equilateral triangle taken in counter clockwise direction. If its circumference is at the origin and z_(1)=1+i , then

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
  1. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

    Text Solution

    |

  2. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

    Text Solution

    |

  3. The vertices of a square are z1,z2,z3 and z4 taken in the anticlockwis...

    Text Solution

    |

  4. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

    Text Solution

    |

  5. if the complex no z1 , z2 and z3 represents the vertices of an equ...

    Text Solution

    |

  6. If P,P^(') represent the complex number z(1) and its additive inverse ...

    Text Solution

    |

  7. Let A(z(1)),B(z(2)),C(z(3)) be the vertices of an equilateral triangle...

    Text Solution

    |

  8. The area of the triangle (in square units) whose vertices are i, omega...

    Text Solution

    |

  9. The complex number z satisfying |z+1|=|z-1| and arg (z-1)/(z+1)=pi/4, ...

    Text Solution

    |

  10. If A,B,C are three points in the Argand plane representing the complex...

    Text Solution

    |

  11. If z(bar(z+alpha))+barz(z+alpha)=0, where alpha is a complex constant,...

    Text Solution

    |

  12. Let A,B,C be three collinear points which are such that AB.AC=1 and th...

    Text Solution

    |

  13. If z1, z2, z3, z4 are the four complex numbers represented by the vert...

    Text Solution

    |

  14. If z be a complex number, then |z-3-4i|^(2)+|z+4+2i|^(2)=k represent...

    Text Solution

    |

  15. In Argand diagram, O, P, Q represent the origin, z and z+ iz respectiv...

    Text Solution

    |

  16. If (2z(1))/(3z(2)) is purely imaginary number, then |(z(1)-z(2))/(z(1)...

    Text Solution

    |

  17. If omega is a cube root of unity then find the value of sin((omega^(10...

    Text Solution

    |

  18. If center of a regular hexagon is at the origin and one of the vertice...

    Text Solution

    |

  19. If z^(2)+(p+iq)z+(r+is)=0, where,p,q,r,s are non-zero, has real roots...

    Text Solution

    |

  20. Let z1, z2, z3 be three vertices of an equilateral triangle circumscri...

    Text Solution

    |