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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2005

  • question_answer
    The  modulus  and  amplitude of \[\frac{1+2i}{1-{{(1-i)}^{2}}}\], are :

    A)  \[\sqrt{2}\] and \[\frac{\pi }{6}\]             

    B)  1 and 0

    C)  1 and \[\frac{\pi }{3}\]                                 

    D)  1 and \[\frac{\pi }{4}\]

    Correct Answer: B

    Solution :

    Let \[z=\frac{1+2i}{1-{{(1-i)}^{2}}}\]                 \[=\frac{1+2i}{1-({{1}^{2}}+{{i}^{2}}-2i)}=\frac{1+2i}{1+2i}\]                 \[=1\]                 \[\therefore \,\,\,|z|=1\] and amp \[(z)={{\tan }^{-1}}\left( \frac{0}{1} \right)=0\]


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