JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Integral power of iota, Algebraic operations and Equality of complex numbers

  • question_answer \[\operatorname{Re}\frac{{{(1+i)}^{2}}}{3-i}\] =

    A) \[-1/5\]

    B) 1/5

    C) 1/10

    D) -1/10

    Correct Answer: A

    Solution :

    \[\operatorname{Re}\left[ \frac{{{(1+i)}^{2}}}{3-i} \right]=\operatorname{Re}\left[ \left( \frac{2i}{3-i} \right)\,\,\left( \frac{3+i}{3+i} \right) \right]\] \[\operatorname{Re}\left[ \frac{{{(1+i)}^{2}}}{3-i} \right]=\operatorname{Re}\left[ \left( \frac{2i}{3-i} \right)\left( \frac{3+i}{3+i} \right) \right]\] \[=\operatorname{Re}\left[ \frac{6i-2}{9+1} \right]=\operatorname{Re}\left[ -\frac{2}{10}+\frac{6}{10}i \right]=-\frac{1}{5}\].


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