A) \[{{z}_{1}}+{{z}_{2}}\]
B) \[{{z}_{1}}-{{z}_{2}}\]
C) \[{{z}_{1}}\times {{z}_{2}}\]
D) \[{{z}_{1}}\div {{z}_{2}}\]
Correct Answer: A
Solution :
This is a parallelogram \[O{{P}_{1}}{{P}_{2}}{{P}_{3}}\]. Then the mid point of \[{{P}_{1}}{{P}_{2}}\] and \[O{{P}_{3}}\] are the same. But midpoint of \[{{P}_{1}}{{P}_{2}}\]is \[\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right)\] So that the coordinates of \[{{P}_{3}}\]are \[\left( {{x}_{1}}+{{x}_{2}},{{y}_{1}}+{{y}_{2}} \right)\] Thus the point \[{{P}_{3}}\] corresponds to sum of the complex number \[{{z}_{1}}\] and \[{{z}_{2}}\]. \[{{\overrightarrow{OP}}_{3}}={{\overrightarrow{OP}}_{1}}+\overrightarrow{{{P}_{1}}{{P}_{3}}}={{\overrightarrow{OP}}_{1}}+{{\overrightarrow{OP}}_{2}}={{z}_{1}}+{{z}_{2}}\]
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