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Math Help - divide polynomial with x+i

  1. #1
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    divide polynomial with x+i

    x^50-20x^32-3x+1 divideed by x+i

    how do u divide by i? can some eplain please.
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  2. #2
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    Quote Originally Posted by gumi View Post
    x^50-20x^32-3x+1 divideed by x+i

    how do u divide by i? can some eplain please.
    When dividing by a complex number, multiply the numerator and denominator by its conjugate.

    For example:

    \frac{10}{4 + 2\,\text{i}}

    =\frac{10\color{red}\left(4 - 2\,\text{i}\right)}{\left(4 + 2\,\text{i}\right)\color{red}\left(4 - 2\,\text{i}\right)}

    =\frac{\color{red}40 - 20\,\text{i}}{\color{red}16 - 4\,\text{i}^2}

    Noting that \text{i}^2 = -1, we have

    \frac{40 - 20\,\text{i}}{16 - {\color{red}(-1)}4}

    =\frac{40 - 20\,\text{i}}{\color{red}20}

    =\frac{40}{20} - \frac{20\,\text{i}}{20}

    =2 - \text{i}

    Does that help?
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  3. #3
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    yes it does thanks
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