I am asked to find $\displaystyle (i-1)^{\frac{1}{17}}$. This is my first class in complex analysis. I used this formula $\displaystyle z^{\frac{1}{n}}= ^n\sqrt{r} \cdot exp [i(\frac{\theta}{n}+\frac{2k\pi}{n})]$ where $\displaystyle k=0, \ldots, n-1$ and I got $\displaystyle ^{34}\sqrt{2} \cdot exp [i(\frac{-\pi}{68}+\frac{2k\pi}{17})] k=0, \ldots, 16$. That's what I got after fully simplfying everything. Is this correct? I just want to make sure I did right.
I am asked to find $\displaystyle (i-1)^{\frac{1}{17}}$. This is my first class in complex analysis. I used this formula $\displaystyle z^{\frac{1}{n}}= ^n\sqrt{r} \cdot exp [i(\frac{\theta}{n}+\frac{2k\pi}{n})]$ where $\displaystyle k=0, \ldots, n-1$ and I got $\displaystyle ^{34}\sqrt{2} \cdot exp [i(\frac{-\pi}{68}+\frac{2k\pi}{17})] k=0, \ldots, 16$. That's what I got after fully simplfying everything. Is this correct? Mr F says: No.
$\displaystyle i - 1 = -1 + i$ therefore $\displaystyle \theta = \frac{3 \pi}{4}$ NOT $\displaystyle - \frac{\pi}{4}$.