# Homework Help: Complex numbers powers and logs

1. Sep 28, 2010

### Liquidxlax

1. The problem statement, all variables and given/known data

not sure how to describe this one, but i need to find the roots.

2. Relevant equations

(r^n)e^(itheta)n = (r^n)cos(thetan) + isin(thetan) n is an element of the reals

3. The attempt at a solution

i'm not sure what to do with this, it is the most weird question on the page. it seems circular to me.

2. Sep 28, 2010

### CalcYouLater

I'm not sure exactly what you are asking here. Here is my attempt at some help.

When dealing with complex numbers, we can use De Moivre's formula to find roots.

$$\alpha={r}{e}^{i\theta}$$

$$\alpha^{\frac{p}{q}}={r}^{\frac{p}{q}}{exp(ip({\theta}+2n{\pi})/q)}$$

Example: Find the roots of

$$i^{\frac{1}{3}}$$

Using:

$$i=e^{\frac{i{\pi}}{2}}$$

And the above equation gives the roots as:

$$e^{\frac{i{\pi}}{6}}$$

$$e^{\frac{5i{\pi}}{6}}$$

$$e^{\frac{9i{\pi}}{6}}$$

I hope that helps.

3. Sep 28, 2010

### Liquidxlax

not really because applying that i still don't get the right answer. I've done many of these types of questions, its just that this one is really weird.

like if i ln and then put it to the e, it is the same thing...

4. Sep 28, 2010

### CalcYouLater

You want to find the roots of a function, right? For which function do you want to find the roots?

5. Sep 29, 2010

### Liquidxlax

-e^ipi i know the answer is -e^(-ipi^2)