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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2007

  • question_answer
    The conjugate of the complex number \[\frac{{{(1+i)}^{2}}}{1-i}\]is

    A)  \[1-i\]                                  

    B)  \[1+i\]

    C)  \[-1+i\]                               

    D)  \[-1-i\]

    Correct Answer: D

    Solution :

    Given complex number is \[\frac{{{(1+i)}^{2}}}{1-i}\] \[=\frac{(1+{{i}^{2}}+2i)}{1-i}\times \frac{1+i}{1+i}\] \[=\frac{2i(1+i)}{1-{{i}^{2}}}\] \[=\frac{2i+2{{i}^{2}}}{1+1}\] \[=\frac{2i-2}{2}\] \[=i-1\] \[\therefore \] Required conjugate is \[-i-1\]


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