The points z_1, z_2, z_3, z_4 in the complex plane are the vertices of a parallelogram taken in o...

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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:
(1) z_1+z_4=z_2+z_3
(2) z_1+z_3=z_2+z_4
(3) z_1+z_2=z_3+z_4
(4) z_1 z_3=z_2 z_4

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