# Thread: Finding principle roots & De Moivre's Theorem?

1. ## 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...

2. ## i am on the samething

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

i feel like exploding

3. 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. :|

4. Originally Posted by bwenner
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 $\displaystyle \alpha=5\text{cis}\left(\frac{\pi}{6}\right)~\&~\b eta=\text{cis}\left(\frac{2\pi}{3}\right)$.
Then the three cube-roots are $\displaystyle \alpha\cdot\beta^0,~\alpha\cdot\beta^1~\&~\alpha\c dot\beta^2$.