Home
Class 12
MATHS
If z1,z2,z3,z4 be the vertices of a para...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

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

If z_1,z_2,z_3,z_4 be the vertices of a quadrilaterla taken in order such that z_1+z_2-z_2+z_3 and |z_1-z_3|=|z_2-z_4| then arg ((z_1-z_2)/(z_3-z_2))= (A) pi/2 (B) +- pi/2 (C) pi/3 (D) pi/6

The points, z_1,z_2,z_3,z_4, in the complex plane are the vertices 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

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

If z_(1), z_(2), z_(3), z_(4) are complex numbers, show that they are vertices of a parallelogram In the Argand diagram if and only if z_(1) + z_(3)= z_(2) + z_(4)

If z_1,z_2,z_3 are vertices of a triangle such that |z_1-z_2|=|z_1-z_3| then arg ((2z_1-z_2-z_3)/(z_3-z_2)) is :

If z_1,z_2,z_3 are vertices of a triangle such that |z_1-z_2|=|z_1-z_3| then arg ((2z_1-z_2-z_3)/(z_3-z_2)) is :

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

If z_1,z_2,z_3 be the vertices A,B,C respectively of triangle ABC such that |z_1|=|z_2|=|z_3| and |z_1+z_2|=|z_1-z_2| then C= (A) pi/2 (B) pi/3 (C) pi/6 (D) pi/4

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then prove that z_1, z_2, z_3, z_4 are concyclic.

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Let A=[1 0 1 1] . Then which of following is not true? (lim)(nvecoo)1/...

    Text Solution

    |

  2. The set of values of lambda for which the vectors vec a=(lambda(log)2...

    Text Solution

    |

  3. If z1,z2,z3,z4 be the vertices of a parallelogram taken in anticlockwi...

    Text Solution

    |

  4. The value of the integral int(pi//3)^(pi//2)x sin(pi[x]-x)dx is (whe...

    Text Solution

    |

  5. If z1, z2, z3 are distinct nonzero complex numbers and a ,b , c in R^...

    Text Solution

    |

  6. Consider I1=int0^(pi//4)e^(x^2)dx ,I2=int0^(pi//4)e^x dx ,I3=int0^(pi/...

    Text Solution

    |

  7. lim(xto0)(sinx^(4)-x^(4)cosx^(4))/(x^(4)(e^(2x^(4))-1-2x^(4))) is

    Text Solution

    |

  8. IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,bn=int0^(pi/2)((sinn x)/(sinx))...

    Text Solution

    |

  9. If A , B ,C are angles of a triangles, then the value of e^(2i A)e^(-i...

    Text Solution

    |

  10. Sum of all the solutions of the equation : tan^2 33x = cos2x - 1 which...

    Text Solution

    |

  11. Statement-1 : Let z be a complex number satisfying |z-3|lt=|z-1|,|z-3|...

    Text Solution

    |

  12. If 0ltaltbltc and the roots alpha,beta of equation a"" x^2+b""x+c="0 a...

    Text Solution

    |

  13. If a^2+b^2=1t h e n(1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+i b

    Text Solution

    |

  14. The graph of the function y=cos xcos(x+2)-cos^2(x+1) is: (A) &n...

    Text Solution

    |

  15. If in a triangle A B C ,(a+b+c)(b+c-a)=kdotb c ,t h e n:

    Text Solution

    |

  16. A round balloon of radius r subtends an angle at the eye of the observ...

    Text Solution

    |

  17. If f^(prime)(1)=-2sqrt(2) and g^(prime)(sqrt(2))=4 , then the derivati...

    Text Solution

    |

  18. Let a(n) be the nth term of an AP, if sum(r=1)^(100)a(2r)= alpha " and...

    Text Solution

    |

  19. Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec axx...

    Text Solution

    |

  20. The fourth term of the sequence 1/(1+sqrt(x)),1/(1-x),1/(1-sqrt(x)), ...

    Text Solution

    |