Find all holomorphic functions $f: \mathbb{C} \rightarrow \mathbb{C}$ such that, for all $x,y\ \epsilon \ \mathbb{R} $ , $Re(f(x+iy)) := 2xy$
So I figured out thus far that $\frac{\partial u}{\partial x}:= 2y$ and $\frac{\partial u}{\partial y}:= 2x$ with $u(x,y):= 2xy$. Now by the Cauchy-Rieman equations I can see that $\frac{\partial v}{\partial y}:= 2y\ $ and $\frac{\partial v}{\partial x}:= -2x\ $ for some $v(x,y)$.
However I seem to be stuck finding $v(x,y)$. Can anybody help me out here, would be very happy.