# Complex roots

1. Sep 10, 2016

### nmsurobert

1. The problem statement, all variables and given/known data
I'm looking for an explanation to something. I've attached a picture of the solution wolfram alpha is giving me.
I understand the first two zeros, +- (-1)^(1/4)*sqrt(2).
But i don't understand the other two zeros with the 3/4 power. Where does that power come from?

This isn't homework but it is course work. I thought I try some of the other problems out before diving into the actual homework and I'm already stuck lol.

2. Relevant equations

3. The attempt at a solution

2. Sep 10, 2016

### Staff: Mentor

Just a few questions: Why don't you supply the link to Wolfram instead? This would definitely result in a better resolution.
Anyway, have you tried to factorize $x^4 + 4$ or to put it another way: what do you know about the roots of unity?

3. Sep 10, 2016

### Staff: Mentor

The wolfram page mentions that these roots are multiples of the four fourth roots of unity (1). The fourth roots of 1 are i, -1, -1, and 1. They are equally spaced around the unit circle.

4. Sep 10, 2016

### nmsurobert

Sorry. I'm on my phone and took a quick screen shot.
I haven't tried to factorize it yet. I'll give that a shot. I know there is some symmetry in factoring problems like that.
I don't know anything about roots of unity.
I figured there was some relation between the first two solutions being 1/4 power and the other two being 3/4 power. I'm assuming "roots of unity" plays a part there.

5. Sep 10, 2016

### nmsurobert

Thanks guys. The book has two pages on roots of unity that help with this problem.