Finding principle roots & De Moivre's Theorem?

**bwenner** · November 18th 2009, 11:16 AM

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...

**coverksa** · November 18th 2009, 11:25 AM

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

i feel like exploding

**bwenner** · November 18th 2009, 11:26 AM

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. :|

**Plato** · November 18th 2009, 02:06 PM

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

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Finding principle roots & De Moivre's Theorem?

i am on the samething

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