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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

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

none of these

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

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

answer is B.

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Detailed Solution

In a parallelogram the midpoints of the two diagonals coincide

$\frac{z_{1} + z_{3}}{2} = \frac{z_{2} + z_{4}}{2} \Rightarrow z_{1} + z_{3} = z_{2} + z_{4}$

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