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

  1. Mar 10, 2010 #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
     
  2. jcsd
  3. Mar 10, 2010 #2

    The Electrician

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  4. Mar 10, 2010 #3
    Sorry, but that actually doesn't help at all. I have no idea what 98% of that article is saying
     
  5. Mar 10, 2010 #4

    The Electrician

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    Do you know what imaginary numbers are? Have you studied complex arithmetic?
     
  6. Mar 11, 2010 #5
    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
     
  7. Mar 11, 2010 #6

    The Electrician

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    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/
     
  8. Mar 11, 2010 #7
    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.
     
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