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

  • question_answer
    If the imaginary part of \[\frac{2z+1}{iz+1}\]is -2, then the locus of the point representing \[z\]in the complex plane is [DCE 2001]

    A) A circle

    B) A straight line

    C) A parabola

    D) None of these

    Correct Answer: B

    Solution :

    We have \[\frac{2z+1}{iz+1}=\frac{2(x+iy)+1}{i(x+iy)+1}=\frac{(2x+1)+2iy}{(1-y)+ix}\] \[=\frac{[(2x+1)(1-y)+2xy]+i[2y(1-y)-x(2x+1)]}{{{(1-y)}^{2}}+{{x}^{2}}}\] But it is given that imaginary part of \[\frac{(2z+1)}{(iz+1)}\]is - 2 Þ\[x+2y-2=0\]. Which is a straight line.


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