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

  • question_answer The imaginary part of  \[\frac{{{(1+i)}^{2}}}{(2-i)}\]is

    A) \[\frac{1}{5}\]

    B) \[\frac{3}{5}\]

    C) \[\frac{4}{5}\]

    D) None of these

    Correct Answer: C

    Solution :

    We have\[\frac{{{(1+i)}^{2}}}{2-i}=\frac{(2i)(2+i)}{(2-i)(2+i)}\]\[=-\frac{2}{5}+i\frac{4}{5}\]. Thus Im \[(z)=\frac{4}{5}\].

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