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

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