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 \[x,y\in R\]and \[(x+iy)(3+2i)=1+i\],  then \[(x,\,y)\] is

    A)   \[\left( 1,\frac{1}{5} \right)\]

    B) \[\left( \frac{1}{13},\frac{1}{13} \right)\]

    C)   \[\left( \frac{5}{13},\frac{1}{13} \right)\]

    D)   \[\left( \frac{1}{5},\frac{1}{5} \right)\]

    Correct Answer: C

    Solution :

    \[x+iy=\left( \frac{1+i}{3+2i} \right)\frac{(3-2i)}{(3-2i)}=\frac{5+i}{13}\] Hence\[x=\frac{5}{13},y=\frac{1}{13}\].

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