Thread: Factoring z^5-1

I have be asked to factorize z^5-1


Attempt at a solution:

z-1 is a factor because 1^5-1=0

So (z-1)(z^4+z^3+z^2+z+1)

I'm not sure how to factor (z^4+z^3+z^2+z+1)

Help please

Originally Posted by ImConfused

I have be asked to factorize z^5-1

This amounts to finding the five fifth roots of one.

Let's agree that .

Then are the roots.

Thus .

You might want to locate the five roots on the unit circle. Remember DeMoivre's theorem? That might help you get a more intuitive grasp of it.