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Math Help - Finding principle roots & De Moivre's Theorem?

  1. #1
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    Finding principle roots & De Moivre's Theorem?

    My math class is possibly the worst arranged class I've ever been in. I think I've said that before on this site. Part of me wants to fail to keep my teacher's reputation realistic, but the other part decided to come here. :>

    I'm stuck on these two things.

    Find the principle root of in polar form.

    aaaand
    Find in rectangular form.


    I have no information to even know where to begin here, since there is no textbook, and this wasn't gone over before in the class. I don't know what to do with the first one, since I think I need values for a and b and the whole thing only seems to be one? And I tried to find R for the second one and ended up with the square root of zero, which seems wrong, so I pretty much stopped there...
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  2. #2
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    Wink i am on the samething

    i am stuck on the same thing i know how it feels


    i feel like exploding
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  3. #3
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    I am wondering if I can simplify the cuberoot125i to 4.33 + 2.5i and then work from there... Trying this now, I'm probably wrong. :|
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  4. #4
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    Quote Originally Posted by bwenner View Post
    I am wondering if I can simplify the cuberoot125i to 4.33 + 2.5i and then work from there... Trying this now, I'm probably wrong. :|
    Let \alpha=5\text{cis}\left(\frac{\pi}{6}\right)~\&~\b  eta=\text{cis}\left(\frac{2\pi}{3}\right).
    Then the three cube-roots are \alpha\cdot\beta^0,~\alpha\cdot\beta^1~\&~\alpha\c  dot\beta^2.
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