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

  • question_answer
    Amplitude of  \[\left( \frac{1-i}{1+i} \right)\] is     [RPET 1996]

    A) -p/2

    B) p/2

    C)   p/4

    D) p/6

    Correct Answer: A

    Solution :

    \[\left( \frac{1-i}{1+i} \right)=\frac{1-i}{1+i}\times \frac{1-i}{1-i}=\frac{{{(1-i)}^{2}}}{2}=\frac{-2i}{2}=-i\] \[\operatorname{Im}(z)<0\], Hence amplitude =\[-\pi /2\].


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