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 \[{{z}_{1}}\] and \[{{z}_{2}}\] be two complex number, then  Re\[({{z}_{1}}{{z}_{2}})=\]

    A) Re \[({{z}_{1}}).\operatorname{Re}({{z}_{2}})\]

    B) Re \[({{z}_{1}})\]. Im \[({{z}_{2}})\]

    C) Im \[({{z}_{1}}).\operatorname{Re}\,({{z}_{2}})\]

    D) None of these

    Correct Answer: D

    Solution :

    If \[{{z}_{1}}\] and \[{{z}_{2}}\] be two complex number then Re \[({{z}_{1}}{{z}_{2}})=\operatorname{Re}({{z}_{1}})\operatorname{Re}({{z}_{2}})-\operatorname{Im}({{z}_{1}})\operatorname{Im}({{z}_{2}})\]


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