(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Complex Numbers: 4th Degree Polynomial

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