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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
    If  \[\frac{5(-8+6i)}{{{(1+i)}^{2}}}=a+ib\], then\[(a,\,b)\] equals [RPET 1986]

    A) (15, 20)

    B) (20, 15)

    C) \[(-15,\,20)\]

    D) None of these

    Correct Answer: A

    Solution :

    \[\frac{5(-8+6i)}{{{(1+i)}^{2}}}=a+ib\]Þ \[\frac{-40+30i}{2i}=15+20i=a+ib\] Equating real and imaginary parts, we get \[a=15\] and\[b=20\].


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