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JEE Main & Advanced Sample Paper JEE Main Sample Paper-29

  • question_answer
    If a complex number z satisfies the equation \[z+\sqrt{2}\left| z+1 \right|+i=0\], where \[i=\sqrt{-1}\], then \[\left| z \right|\] is equal to

    A) 1                                             

    B) 2

    C) \[\sqrt{3}\]                                        

    D) \[\sqrt{5}\]

    Correct Answer: D

    Solution :

    Put \[z=x+iy,\] we get \[\left( x+\sqrt{2}.\sqrt{{{(x+1)}^{2}}+y} \right)+i(y+1)=0+i0\] \[\therefore \]On equating real and imaginary parts, we get \[x+\sqrt{2}.\sqrt{{{(x+1)}^{2}}+{{y}^{2}}}=0\] and \[y+1=0\] so, on solving (i) and (ii), we get \[x=-2,\,\,y=-1\] \[\therefore z=-2-i\Rightarrow |z|\,\,=\sqrt{5}\]


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