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Math Help - complex solutions

  1. #1
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    complex solutions

    Could someone help me with this?
    Find all solutions to z = (6 − 6√3)^(1/5).
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  2. #2
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    Quote Originally Posted by frankdent1 View Post
    Could someone help me with this?
    Find all solutions to z = (6 − 6√3)^(1/5).
    I am guessing you mean z=6(1-i\sqrt{3})

    we use De Moivre's formula

    z^{\frac{1}{n}}=r^{\frac{1}{n}}\left[ \cos(\frac{x+2\pi k}{n})+ i \sin(\frac{x+2\pi k}{n})\right]

    in the above formula x is the reference angle so ours is -\frac{\pi}{3} r is the radius(=6) and k goes from 0 to n-1

    z^{\frac{1}{5}}=6^{\frac{1}{5}}\left[ \cos(\frac{-\frac{\pi}{3}+2\pi k}{6})+ i \sin(\frac{-\frac{\pi}{3}+2\pi k}{6})\right]

    if you plug in k=0,1,2,3,4,5 you will get all solutions
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