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Question: The points \(z_{1},z_{2},z_{3},z_{4}\) in the complex plane are the vertices of a parallelogram take...

The points z1,z2,z3,z4z_{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

z1+z4=z2+z3z_{1} + z_{4} = z_{2} + z_{3}

B

z1+z3=z2+z4z_{1} + z_{3} = z_{2} + z_{4}

C

z1+z2=z3+z4z_{1} + z_{2} = z_{3} + z_{4}

D

None of these

Answer

z1+z3=z2+z4z_{1} + z_{3} = z_{2} + z_{4}

Explanation

Solution

Sol. Diagonals of a parallelogram ABCD are bisected each other at a point i.e*.,* z1+z32=z2+z42\frac{z_{1} + z_{3}}{2} = \frac{z_{2} + z_{4}}{2} ⇒ z1+z3=z2+z4.z_{1} + z_{3} = z_{2} + z_{4}.