Please see my EMFT online notes.
Where it says I assumed $\hat{V}(x)$ to be real-valued out of laziness. But down lower where a general solution for $\hat{V}(x)$ is given, it appears that $V(x)$ could take on complex values for some coefficients and points $x$ along the transmission line. The book I'm using just jumps right over this as if it's obvious, and doesn't even say whether it should be real or complex-valued.