JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Geometry of complex numbers

  • question_answer
    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

    Correct Answer: B

    Solution :

    Diagonals of a parallelogram \[ABCD\]are bisected each other at a point i.e.\[\frac{{{z}_{1}}+{{z}_{3}}}{2}=\frac{{{z}_{2}}+{{z}_{4}}}{2}\]Þ \[{{z}_{1}}+{{z}_{3}}={{z}_{2}}+{{z}_{4}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner