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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 values of \[x\] and \[y\] satisfying the equation \[\frac{(1+i)x-2i}{3+i}\] \[+\frac{(2-3i)\,y+i}{3-i}=i\] are [IIT 1980; MNR 1987]

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

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

    C) \[x=0,\,y=1\]

    D) \[x=1,y=0\]

    Correct Answer: B

    Solution :

    \[\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i\] Þ \[(4+2i)x+(9-7i)y-3i-3=10i\] Equating real and imaginary parts, we get \[2x-7y=13\] and\[4x+9y=3\]. Hence \[x=3\]and\[y=-1\]. Trick : After finding the equations, no need to solve them, put the values of \[x\] and \[y\] given in the options and get the appropriate option.


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