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 \[\frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy}\], then

    A) \[x=1,y=-3\]

    B) \[x=-1,y=3\]

    C) \[x=1,y=3\]

    D) \[x=-1,y=-3\]or \[x=1,\]\[y=3\]

    Correct Answer: D

    Solution :

    Given that \[\frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy}\] Þ  \[24{{x}^{2}}+9ixy-6{{y}^{2}}+16ixy=75i-30\] Þ  \[24{{x}^{2}}-6{{y}^{2}}+25ixy=75i-30\] Equating real and imaginary parts, we get \[24{{x}^{2}}-6{{y}^{2}}=-30\]or \[4{{x}^{2}}-{{y}^{2}}=-5\]and \[xy=3\] On solving we get \[x=\pm 1,y=\pm 3\]

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