First slide

Geometry of complex numbers

Question

The point $z_{1}, z_{2}, z_{3}, z_{4}$ in the complex plane are the vertices of a parallelogram taken in order if and only if

Easy

A

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

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

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

none of these

Solution

Diagonals of a parallelogram are bisect each other.
$\frac{z_{1} + z_{3}}{2} = \frac{z_{2} + z_{4}}{2} \Rightarrow z_{1} + z_{3} = z_{2} + z_{4}$

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