On complete arcs arising from plane curves

We show that the set of $\fq$-rational points of either certain Fermat curves or certain $\fq$-Frobenius non-classical plane curves is a complete $(k,d)$-arc in $\P^2(\fq)$, where $k$ and $d$ are respectively the number of $\fq$-rational points and the degree of the underlying curve.