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

  • question_answer
    Solving \[3-2yi={{9}^{x}}-7i\], where \[{{i}^{2}}=-1,\] for x and y real, we get [AMU 2000]

    A) \[x=0.5\,\,,\,\,y=3.5\]

    B) \[x=5\,\,,\,\,y=3\]

    C) \[x=\frac{1}{2}\,\,,\,\,y=7\]

    D) \[x=0,\,y=\frac{3+7i}{2i}\]

    Correct Answer: A

    Solution :

    \[3-2yi={{9}^{x}}-7i\] Equating real and imaginary parts both sides \[{{9}^{x}}=3\Rightarrow \,{{3}^{2x}}={{3}^{1}}\Rightarrow 2x=1\Rightarrow x=0.5\] \[2y=7\Rightarrow \,y=3.5\].

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