For question 20, you just need an f to satisfy that equation. In other words, you need an f such that dF/dx=f and dF/dy=if. This means that dF/dx=-i(dF/dy). This is a differential equation that can be satisfied by e^(y-ix+c)+c. I'm not 100% sure about it but it seems right. I got the same thing as you did for 17.