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 \[(1-i)x+(1+i)y=1-3i,\] then  \[(x,y)=\]

    A) \[(2,-1)\]

    B) \[(-2,\,1)\]

    C) \[(-2,-1)\]

    D) (2, 1)

    Correct Answer: A

    Solution :

    \[(1-i)x+(1+i)y=1-3i\]\[\Rightarrow \] \[(x+y)+i\,(-x+y)=1-3\,i\] Equating real and imaginary parts, we get \[x+y=1\]and\[-x+y=-3\];  \[\therefore \] \[x=2,y=-1\]. Thus point is\[(2,\,-1)\].

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