Suppose f is an analytical function of the complex variables given by:
where g(x,y) is a real valued function of real variables x and y. If g(2,3)=1, then g(7,3)=?
From reading my book, I understand this going to be treated somewhat similar to a solving a differential equation; however, I am not sure what to do. I haven't made it to this section yet in Complex Analysis but in a week I have the GRE Math Subject Test and this is a practice question.
Maybe we can state the Cauchy-Riemann equations. They're easy to understand.
Let . We have that is analytic if and only if and (simultaneously).
Now, to apply these to your question, you know that , , , and . From the equations above, we have and . You can integrate to recover . Don't forget to use to get the constant of integration.
Give it a try.