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Math Help - Complex Roots

  1. #1
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    Complex Roots

    I am asked to find (i-1)^{\frac{1}{17}}. This is my first class in complex analysis. I used this formula z^{\frac{1}{n}}= ^n\sqrt{r} \cdot exp [i(\frac{\theta}{n}+\frac{2k\pi}{n})] where k=0, \ldots, n-1 and I got ^{34}\sqrt{2} \cdot exp [i(\frac{-\pi}{68}+\frac{2k\pi}{17})] k=0, \ldots, 16. That's what I got after fully simplfying everything. Is this correct? I just want to make sure I did right.
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  2. #2
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    Quote Originally Posted by xboxlive89128 View Post
    I am asked to find (i-1)^{\frac{1}{17}}. This is my first class in complex analysis. I used this formula z^{\frac{1}{n}}= ^n\sqrt{r} \cdot exp [i(\frac{\theta}{n}+\frac{2k\pi}{n})] where k=0, \ldots, n-1 and I got ^{34}\sqrt{2} \cdot exp [i(\frac{-\pi}{68}+\frac{2k\pi}{17})] k=0, \ldots, 16. That's what I got after fully simplfying everything. Is this correct? Mr F says: No.

    I just want to make sure I did right.
    i - 1 = -1 + i therefore \theta = \frac{3 \pi}{4} NOT  - \frac{\pi}{4}.
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