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Math Help - Dividing Complex Numbers

  1. #1
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    Question Dividing Complex Numbers

    Okay I have established that you multiply by the denomonator after changing it's sign. For example
    3-2i (3-2i)(5-i)
    ____ = _________
    5+i (5+i)(5-i)



    My question is how do I solve

    2+i
    ____
    i
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by KeiaBlake View Post
    Okay I have established that you multiply by the denomonator after changing it's sign. For example
    3-2i (3-2i)(5-i)
    ____ = _________
    5+i (5+i)(5-i)



    My question is how do I solve

    2+i
    ____
    i
    Just multiply the numerator and denominator by i:

    \frac{2+i}{i}=\frac{2i+i^2}{i^2}=\frac{2i-1}{-1}=\color{red}\boxed{1-2i}

    Does this make sense?

    --Chris
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