ExamHabit
Practise free

1983

JEE Main 1983 Mathematics question on Complex Numbers and Quadratic Equations

The points z1,z2,z3z_1, z_2, z_3 and z4z_4 in the complex plane are the vertices of a parallelogram taken in order, if and only if
  1. A.
    z1+z4=z2+z3z_1 + z_4 = z_2 + z_3
  2. B.
    z1+z3=z2+z4z_1 + z_3 = z_2 + z_4
  3. C.
    z1+z2=z3+z4z_1 + z_2 = z_3 + z_4
  4. D.
    None of these
Show answer and solution

Correct option: B

Solution

In a parallelogram, the diagonals bisect each other, so their midpoints must coincide. For vertices z₁, z₂, z₃, z₄ taken in order, the diagonals are z₁z₃ and z₂z₄. Setting their midpoints equal: (z₁ + z₃)/2 = (z₂ + z₄)/2, which gives z₁ + z₃ = z₂ + z₄. This is the necessary and sufficient condition for the quadrilateral to be a parallelogram.

[1983]

Practise Complex Numbers and Quadratic Equations the way it is asked

A timed set of real JEE Main Complex Numbers and Quadratic Equations questions, graded as the exam grades. No sign-up.

Start a Complex Numbers and Quadratic Equations test

More: all JEE Main Complex Numbers and Quadratic Equations questions · JEE Main 1983 · Mathematics chapter list