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

  • question_answer
    The equation \[\overline{b}z+b\overline{z}=c,\]where \[b\] is a non-zero complex constant and c is real, represents

    A) A circle

    B)  A straight line

    C) A parabola

    D) None of these

    Correct Answer: B

    Solution :

    Equation \[\overline{b}z+b\overline{z}=c\] Putting \[z=x+iy,b={{b}_{1}}+i{{b}_{2}}\] where \[x,y,\,\,{{b}_{1}},{{b}_{2}}\] are real, then the given equation become \[({{b}_{1}}-i{{b}_{2}})(x+iy)+({{b}_{1}}+i{{b}_{2}})(x-iy)=c\] or \[2{{b}_{1}}x+2{{b}_{2}}y=c\] Which is equation of a straight line. Note: It is a fundamental concept.


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