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

z_{1} + z_{4} = z_{2} + z_{3}

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z_{1} + z_{3} = z_{2} + z_{4}

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z_{1} + z_{2} = z_{3} + z_{4}

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none ofthese

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Solution

The correct option is B $z_{1} + z_{3} = z_{2} + z_{4}$
The points $z_{1}, z_{2}, z_{3}, z_{4}$ in the complex plane are the vertices of a parallelogram.
Let $A B C D$ be the parallelogram
In a parallelogram diagonals bisect each other.Hence mid-point of $A C$ and $B D$ is same.
$\Rightarrow \frac{z_{1} + z_{3}}{2} = \frac{z_{2} + z_{4}}{2}$
$\Rightarrow z_{1} + z_{3} = z_{2} + z_{4}$
Hence, option B.

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