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

  • question_answer
    If the vertices of a quadrilateral be \[A=1+2i,\] \[B=-3+i,\] \[C=-2-3i\] and \[D=2-2i\],  then the quadrilateral is

    A) Parallelogram

    B) Rectangle

    C) Square

    D) Rhombus

    Correct Answer: C

    Solution :

    Given the vertices of quadrilateral \[A(1+2i),B(-3+i),C(-2-3i)\]and \[D(2-2i)\] Now, \[AB=\sqrt{16+1}=\sqrt{17},BC=\sqrt{16+1}=\sqrt{17}\] \[CD=\sqrt{16+1}=\sqrt{17,}\,DA=\sqrt{16+1}=\sqrt{17}\] \[AC=\sqrt{9+25}=\sqrt{34},\,BD=\sqrt{25+9}=\sqrt{34}\]   Hence it is a square.


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