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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2007

  • question_answer
    The imaginary part of \[{{i}^{i}}\]is

    A) \[0\]                                     

    B)  \[1\]

    C)  \[2\]                                    

    D)  \[-1\]

    Correct Answer: A

    Solution :

    Let  \[(a+ib)={{i}^{i}}\] Taking log on both sides, we get                 \[\log (a+ib)=i\,log\,i\] \[\Rightarrow \]               \[\log (a+ib)=(i\,\,\pi /2)\] \[\Rightarrow \]               \[\log (a+ib)=-\frac{\pi }{2}\] \[\Rightarrow \]               \[(a+ib)={{e}^{-\pi /2}}\] On comparing imaginary part of \[{{i}^{i}}\] is 0.


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