Try to solve a first order linear partial differential equation $P(x,\partial)u(x)=f(x)$ in complex domain, while the operator is of the following form: $$ P=a_0+a_1x_1\partial_{x_1}+\cdots+a_nx_n\partial_{x_n}, $$ where~$(a_0,\cdots,a_n)\in R^{n+1}$, $x=(x_1,\cdots,x_n)\in C^n$.
In a real domain, we can use the well-known characteristic methods to give a general solution. However, I am looking for some fundamental references for the complex case, please show me if you have any suggestions.