Determining conjugate roots (1 Viewer)

[coca cola]

Is there any general pattern for determining conjugate roots in roots of unity, without having to result to trig?

Like if I have w as a complex 5th root of unity , then how can I find out its conjugate without using trigonometry?

 

[coca cola]

Ahh don't worry, figured it out.

 

[Shuter]

Don't share answers or anything.

 

[coca cola]

I thought it was obvious, I just forgot the method.

Just use a circle then place each of the solutions on it starting from one, like 1, w, w^2, w^3, w^4, which are equally spaced, then you'll see conjugate of w = w^4, and conjugate of w^2 = w^3. Then use this fact to do those root and coeffecient relationship questions.