RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    If\[z=x+iy,\]then \[z\overline{z}+2(z+\overrightarrow{z})+c=0\]will define a

    A)  circle             

    B)  straight line

    C)  parabola          

    D)  point

    Correct Answer: A

    Solution :

     If \[z=x+iy\Rightarrow z\overline{z}+2(z+\overline{z})+c=0\] \[\Rightarrow \] \[(x+iy)(x-iy)+2[(x+iy)\] \[+(x-iy)]+c=0\] \[\Rightarrow \] \[{{x}^{2}}-{{i}^{2}}{{y}^{2}}+2[2x]+c=0\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}+4x+c=0\] which represents the equation of circle.


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