(B) In a parallelogram $ABCD$,the diagonals $AC$ and $BD$ bisect each other at the same midpoint.The midpoint of diagonal $AC$ is given by $\frac{z_1

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(B) In a parallelogram $ABCD$,the diagonals $AC$ and $BD$ bisect each other at the same midpoint.The midpoint of diagonal $AC$ is given by $\frac{z_1 + z_3}{2}$.The midpoint of diagonal $BD$ is given by $\frac{z_2 + z_4}{2}$.Since the diagonals bisect each other,we have $\frac{z_1 + z_3}{2} = \frac{z_2 + z_4}{2}$.Therefore,$z_1 + z_3 = z_2 + z_4$.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

Medium

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

IIT 1981 All IIT

IIT 1983 All IIT

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

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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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