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

  • question_answer If \[{{z}_{1}}=1-i\] and \[{{z}_{2}}=-2+4i\],  then  \[\operatorname{Im}\left( \frac{{{z}_{1}}{{z}_{2}}}{{{z}_{1}}} \right)=\]

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: D

    Solution :

    If\[{{z}_{1}}=1-i\]and  \[{{z}_{2}}=-2+4i\] Then\[\frac{{{z}_{1}}{{z}_{2}}}{{{z}_{1}}}=\frac{(1-i)(-2+4i)}{1-i}=-2+4i\]Þ \[\operatorname{Im}\left( \frac{{{z}_{1}}{{z}_{2}}}{{{z}_{1}}} \right)=4\].

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