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, 1983; UPSEAT 2004]

\[{{z}_{1}}+{{z}_{4}}={{z}_{2}}+{{z}_{3}}\]

\[{{z}_{1}}+{{z}_{3}}={{z}_{2}}+{{z}_{4}}\]

The points \[{{z}_{1}},\,{{z}_{2}},\,{{z}_{3}},\,{{z}_{4}}\] in the co

1.	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, 1983; UPSEAT 2004]
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
Answer» C. \[{{z}_{1}}+{{z}_{2}}={{z}_{3}}+{{z}_{4}}\]

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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 [IIT 1981, 1983; UPSEAT 2004]

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