solution to the PDE $\frac{\partial f}{\partial x} + i\frac{\partial f}{\partial y} = g$? where g is k times continuously differentiable function

Question

How can I find the solution (in $C^k$) to the complex PDE $\frac{\partial f}{\partial x} + i\frac{\partial f}{\partial y} = g$? where g is (1) complex-valued, (2) k times continuously differentiable function and (3) with compact support.

I didn't learn any PDE techniques but this is an exercise in my complex variable text.