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 :
Let \[{{z}_{1}},\,\,{{z}_{2}}\,\,{{z}_{3}}\,\,and\,\,{{z}_{4}}\] the points in complex lane be the vertices of a parallelogram taken in order. Since the diagonals of a parallelogram bisect, hence the mid points of AC and BD must coincide i.e., \[\frac{{{z}_{1}}+{{z}_{3}}}{2}=\frac{{{z}_{2}}+{{z}_{4}}}{2}\,\,\Rightarrow \,\,{{z}_{1}}+{{z}_{3}}={{z}_{2}}+{{z}_{4}}\]You need to login to perform this action.
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