Originally Posted by

**roninpro** Maybe we can state the Cauchy-Riemann equations. They're easy to understand.

Let $\displaystyle f(x,y)=u(x,y)+i v(x,y)$. We have that $\displaystyle f$ is analytic if and only if $\displaystyle u_x=v_y$ and $\displaystyle u_y=-v_x$ (simultaneously).

Now, to apply these to your question, you know that $\displaystyle u_x=2$, $\displaystyle u_y=3$, $\displaystyle v_x=g_x$, and $\displaystyle v_y=g_y$. From the equations above, we have $\displaystyle 2=g_y$ and $\displaystyle 3=-g_x$. You can integrate to recover $\displaystyle g$. Don't forget to use $\displaystyle g(2,3)=1$ to get the constant of integration.

Give it a try.