Rationalizing fractions over finite fields

[burritoloco]

Homework Statement

Let w be a primitive n-th root of unity in some finite field. Let 0 < k < n. My question is how to rationalize

[\tex]\dfrac{1}{1 + w^k}[\tex].

That is, can we get rid of the denominator somehow? I know what to do in the case of complex numbers but here I'm at a loss. Thanks!

Homework Equations

The Attempt at a Solution

 

[burritoloco]

Not sure what is the command for latex but I meant 1/(1 + w^k).

 

[SteamKing]

Isn't (1 + w^k) a complex number?

 

[burritoloco]

It isn't. It's in a finite field.