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

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

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

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
Gold Member
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/

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.