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Math Help - [SOLVED] Complex Polynomial Division

  1. #1
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    [SOLVED] Complex Polynomial Division



    However, this is wrong. It should be z^2+zi-1. I'm not sure how one would arrive here, however.
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    Thumbs down

    Wait, nevermind. I see it now. Stupid mistake. Sorry.
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    Quote Originally Posted by davismj View Post


    However, this is wrong. It should be z^2+zi-1. I'm not sure how one would arrive here, however.
    Try using the Difference of Two Cubes Rule:

    z^3 + i = z^3 - (-i)

     = z^3 - i^3

     = (z - i)(z^2 + iz + i^2)

     = (z - i)(z^2 + iz - 1).


    So \frac{z^3 + i}{z - i} = \frac{(z - i)(z^2 + iz - 1)}{z - i}

     = z^2 + iz - 1.
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