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JCECE Engineering JCECE Engineering Solved Paper-2003

  • question_answer
    If the-complex number \[{{z}_{1}},\,\,{{z}_{2}}\] and \[{{z}_{3}}\] represent the vertices of an equilateral triangle such that \[|{{z}_{1}}|=|{{z}_{2}}|=|{{z}_{3}}|\], then \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\] is equal to:

    A) \[0\]                                     

    B) \[1\]

    C) \[-1\]                                    

    D)  none of these

    Correct Answer: A

    Solution :

    Let the complex numbers \[{{z}_{1}},\,\,{{z}_{2}},\,\,{{z}_{3}}\] denotes the vertices \[A,\,\,B,\,\,C\] of an equilateral triangle \[ABC\], then if \[O\] be the origin we have                 \[\overline{OA}={{z}_{1}},\,\,\overline{OB}={{z}_{2}},\,\,\overline{OC}={{z}_{3}}\] \[\therefore \]  \[|{{z}_{1}}||{{z}_{2}}||{{z}_{3}}|\] \[\Rightarrow \]               \[OA=OB=OC\] \[\therefore \]\[O\]is the circumcentre of \[\Delta \,\,ABC\], hence\[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]


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