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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2009

  • question_answer
    If\[\frac{x-1}{1+i}+\frac{y-1}{1-i}=i,\]where\[x\]and y are real numbers and\[i=\sqrt{-1},\]then

    A)  \[x=0\]            

    B)  \[x<0\]

    C)  \[x>0\]            

    D)  None of these

    Correct Answer: A

    Solution :

     Given, \[\frac{x-1}{1+i}+\frac{y-1}{1-i}=i\] \[\Rightarrow \] \[(1-i)(x-1)+(y-1)(1+i)=2i\] \[\Rightarrow \] \[x-1-ix+i+y+yi-1-i=2i\] \[\Rightarrow \] \[x+y-2+i(y-x-2)=0\] \[\Rightarrow \] \[x+y-2=0\]and \[y-x-2=0\] \[\Rightarrow \] \[x=0,y=2\]


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