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JEE Main & Advanced AIEEE Solved Paper-2008

  • question_answer
    The conjugate of a complex number is \[\frac{1}{i-1}\]. Then that complex number is       AIEEE  Solved  Paper-2007

    A) \[\frac{-1}{i+1}\]

    B)                        \[\frac{1}{i-1}\]                

    C)        \[\frac{-1}{i-1}\]                              

    D) \[\frac{1}{i+1}\]

    Correct Answer: A

    Solution :

                    \[z=\frac{1}{i-1}\Rightarrow z=\frac{i+1}{-2}\]    \[\Rightarrow \]               \[\overline{z}=\frac{1-i}{-2}=\frac{\left( 1-i \right)\left( i+1 \right)}{-2\left( i+1 \right)}\Rightarrow -\frac{1}{i+1}\]


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