Home
Class 12
MATHS
Find the relation if z1, z2, z3, z4 are ...

Find the relation if `z_1, z_2, z_3, z_4` are the affixes of the vertices of a parallelogram taken in order.

Text Solution

Verified by Experts

As the diagonal of a parallelogram bisect each other, therefore, comnplex number of the mid-point of AC is same the complex number of the mid point of BD.

`therefore (z_(1) + z_(3))/(2) = (z_(2) + z_(4))/(2)`
or `z_(1) + z_(3) = z_(2) + z_(4)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise SLOVED EXAMPLES|15 Videos
  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.1|4 Videos
  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos
  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

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 represent the vertices of a rhombus in anticlockwise order, then

If z_1, z_2, z_3 be the affixes of the vertices A, B and C of a triangle having centroid at G such that z = 0 is the mid point of AG then 4z_1 + z_2 + z_3 =

On the Argand plane z_1, z_2a n dz_3 are respectively, the vertices of an isosceles triangle A B C with A C=B C and equal angles are thetadot If z_4 is the incenter of the triangle, then prove that (z_2-z_1)(z_3-z_1)=(1+sectheta)(z_4-z_1)^2dot

If A(z_1),B(z_2),C(z_3) and D(z_4) be the vertices of the square ABCD then

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

Given that the complex numbers which satisfy the equation | z bar z ^3|+| bar z z^3|=350 form a rectangle in the Argand plane with the length of its diagonal having an integral number of units, then area of rectangle is 48 sq. units if z_1, z_2, z_3, z_4 are vertices of rectangle, then z_1+z_2+z_3+z_4=0 rectangle is symmetrical about the real axis a r g(z_1-z_3)=pi/4or(3pi)/4

If (x_(1),y_(1),z_(1)) , (x_(2),y_(2),z_(2)) , (x_(3) ,y_(3),z_(3)) and (x_(4) , y_(4) , z_(4)) be the consecutive vertices of a parallelogram, show that x_(1)+x_(3)=x_(2)+x_(4),y_(1)+y_(3)=y_(2)+y_(4) and z_(1)+z_(3)=z_(2)+z_(4) .

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
  1. If z = x + iy lies in the third quadrant, then prove that (barz)/(z) ...

    Text Solution

    |

  2. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

    Text Solution

    |

  3. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

    Text Solution

    |

  4. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

    Text Solution

    |

  5. Find real values of x and y for which the complex numbers -3+i x^2y an...

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

    Text Solution

    |

  8. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0,w ...

    Text Solution

    |

  9. Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is eithe...

    Text Solution

    |

  10. Find the square root of the following: 5+12 i

    Text Solution

    |

  11. Evaluate : i^(135)

    Text Solution

    |

  12. Solve for z : z^2-(3-2i)z=(5i-5)dot

    Text Solution

    |

  13. Solve the equation (x-1)^3+8=0 in the set C of all complex numbers.

    Text Solution

    |

  14. If n is n odd integer that is greater than or equal to 3 but not a mul...

    Text Solution

    |

  15. omega is an imaginary root of unity. Prove that If a+b+c = 0 th...

    Text Solution

    |

  16. Find the complex number omega satisfying the equation z^3-8i and lying...

    Text Solution

    |

  17. (1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1...

    Text Solution

    |

  18. If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-...

    Text Solution

    |

  19. Let z(1)= cos 12^(@) + I sin 12^(@) and z(2) = cos 48^(@) + i. sin 4...

    Text Solution

    |

  20. Covert the complex number z = 1 + cos (8pi)/(5) + i. sin (8pi)/(5) in ...

    Text Solution

    |