3 cube roots, 4 fourth roots, and N nth-roots of -1

[MWidhalm18]

My "Computational World" class is supposedly an intro to computer science without programming, but the questions are all over the place. I'm completely stuck on this question:

Show expressions for:
(a). 3 cube roots of -1
(b). 4 fourth roots of -1
(c). In the general case, N nth-roots of -1

My professor said that we could use graphs with vectors. He showed us an example of the 3 cube roots of 1, but I have no idea what any of that meant. I unfortunately have no work to show for my attempt because I have no idea what he means. Please help

 

[The Electrician]

Everything you need to know is explained here:

http://en.wikipedia.org/wiki/Root_of_unity

 

[MWidhalm18]

Everything you need to know is explained here:

http://en.wikipedia.org/wiki/Root_of_unity

Sorry, but that actually doesn't help at all. I have no idea what 98% of that article is saying

 

[The Electrician]

Do you know what imaginary numbers are? Have you studied complex arithmetic?

 

[MWidhalm18]

Do you know what imaginary numbers are? Have you studied complex arithmetic?

The class is a 1000 level course and the professor assumes absolutely no mathematical or physics knowledge beforehand. I have taken algebra, trig, and calc but it was at least 2 years ago and I don't want to make the problem harder than I need to. It's very basic

 

[The Electrician]

Boy, this is going to be a tough one. I don't know how you can represent all the nth roots of -1 without the use of imaginary (or complex) numbers.

To find these roots uses the square root of -1, otherwise you just can't do it.

Here are some links to show the use of graphs and vectors to represent imaginary numbers. Maybe they will help.

http://en.wikipedia.org/wiki/Argand_diagram

http://www.daviddarling.info/encyclopedia/A/Argand_diagram.html

http://demonstrations.wolfram.com/ArgandDiagram/

 

[xaos]

form the corresponding polynomial equation and find all the roots through analytic factoring. for n=1...4 this isn't too difficult, but for larger n, i wouldn't do this. at the very least you need to know what complex number is and why they come up in polynomial equations.