1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Complex Numbers: 4th Degree Polynomial

  1. Aug 7, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve the following equation:

    [tex]z^4+z^3+z^2+z+1 = 0[/tex]

    z is a complex number.

    2. The attempt at a solution
    I was trying to factorize it to 1st degree polynomial multiplied by 3rd degree polynomial:
    [tex](z+a)(z^3+bz^2+cz+1/a) = 0[/tex]
    I discovered that I need to solve 3rd degree polynomial just to do that.
    [tex]a^3-a^2+1 = 0[/tex]
    This is too much mess for a small homework exercise. I think that there is a technique that I am not aware of.

    Thank You.
  2. jcsd
  3. Aug 7, 2010 #2
    Try multiplying the original equation by z - 1.
  4. Aug 7, 2010 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The lesson here is that you shouldn't forget what you learned in earlier classes. That polynomial is a geometric series, is it not?
  5. Aug 7, 2010 #4
    @Hurkyl Very perceptive of you ! :)

    Through the use of the finite geometric series sum you can find all the roots !

    @Petek it's the same as multiplying by (1-z), you right.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook