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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Conjugate, Modulus and Argument of complex number

  • question_answer
    The modulus and amplitude of \[\frac{1+2i}{1-{{(1-i)}^{2}}}\] are  [Karnataka CET 2005]

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

    B) 1 and 0

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

    D) 1 and \[\frac{\pi }{4}\]

    Correct Answer: B

    Solution :

    \[\frac{1+2i}{1-{{(1-i)}^{2}}}=\frac{1+2i}{1-(1-1-2i)}=\frac{1+2i}{1+2i}=1+0i\] Modulus =1 Amplitude \[\theta \]=\[{{\tan }^{-1}}\frac{0}{1}=0\].


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