Complex NumbersHard

Question

The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order, if and only if

Options

A.z1 + z4 = z2 + z3
B.z1 + z3 = z2 + z4
C.z1 + z2 = z3 + z1
D.None of these

Solution

        
Since, z1, z2, z3, z1 are the vertices of parallelogram.
∴ Mid point of AC = mid point of BD
⇒
⇒ z1 + z3 = z2 + z4

Create a free account to view solution

View Solution Free
Topic: Complex Numbers·Practice all Complex Numbers questions

More Complex Numbers Questions

If 1, α1, α2, α3, .....α8, are nine, ninth roots of unity (taken in counter-clockwise sequence) then...The amplitude of 3 − √8 is -...The set of points on an Arg and diagram which satisfy both | z | ≤ 4 & Arg z = π/3 are lying on -...If the vertices of an equilateral triangle are situated at z = 0, z = z1, z = z2, then which of the following is/are tru...If |z1 + z2|2 = |z1|2 + |zz|2 then...