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
Correct Answer: B
Solution :
Key Idea: Diagonals of a parallelogram bisect each other at the same point. Since, the points \[{{z}_{1}},{{z}_{2}},{{z}_{3}}\]and \[{{z}_{4}}\] are the vertices of a parallelogram, therefore diagonals of a parallelogram bisect each other at a point \[\frac{{{z}_{1}}+{{z}_{3}}}{2}=\frac{{{z}_{2}}+{{z}_{4}}}{2}\] \[\Rightarrow \] \[{{z}_{1}}+{{z}_{3}}={{z}_{2}}+{{z}_{4}}\]
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