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Manipal Engineering Manipal Engineering Solved Paper-2008

  • 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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