In Springer's Encyclopaedia of Mathematics> Galois Cohomology, it is mentioned that
For an imperfect field $k$, $H^1(k,\mathbb{G}_a)\neq 0$ in general.
I'm looking for such an example or a reference to one.
(Here $\mathbb{G}_a$ is the additive group of a field and $H^1(k,\mathbb{G}_a)$ means the first cohomology of the Galois group of $K/k$ with values in $\mathbb{G}_a$, where $K$ is the separable algebraic closure of $k$)
Many Thanks!