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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

  • question_answer
    The value of \[{{i}^{i}}\]is:

    A)  \[\omega \]                                      

    B)  \[-{{\omega }^{2}}\]

    C)  \[\pi /2\]                            

    D)  none of these

    Correct Answer: D

    Solution :

    Let \[A={{i}^{i}}\Rightarrow \log A=i\log i\] \[\Rightarrow \]\[\log A=i\log (0+i)=i[\log 1+i{{\tan }^{-1}}\infty ]\] \[\Rightarrow \]\[\log A=i\,[0+i\pi /2]=-\pi /2\] \[\Rightarrow \]\[A={{e}^{-\pi /2}}\]


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