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Math Help - imaginary number question

  1. #1
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    imaginary number question

    I feel like this is probably a simple problem, but i'm stumped.
    the question is "Write the expression in standard form"
    \frac{(2+i)^2(-i)}{1+i}

    I know the standard form, it's just that when I divide my answer doesn't match the answer in the back of the book which is \frac{1}{2}-\frac{7}{2i}
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  2. #2
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    All yu need to do is exapnd the numerator and then multiply both numerator and denominator by the conmplex conjugate


    \frac{(2+i)^2(-i)}{1+i}

    \frac{(2+i)^2(-i)}{1+i}

    = \frac{(4+4i+i^2)(-i)}{1+i}

     = \frac{(4+4i-1)(-i)}{1+i}

     = \frac{(3+4i)(-i)}{1+i}

     = \frac{-3i-4i^2}{1+i}

     = \frac{-3i+4}{1+i}

    then

     = \frac{-3i+4}{1+i}\times \frac{1-i}{1-i}

    can you finish?
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