For which values $a, b \in \mathbb{R}$ the function $u(x,y) = ax^2+2xy+by^2$ is it the real part of a holomorphic function in $\mathbb{C}$ 
For which values $a, b \in \mathbb{R}$ the function $$u(x,y) =
 ax^2+2xy+by^2$$ is  the real part of a holomorphic function in
  $\mathbb{C}$.

I think we have to take Cauchy-Riemann theorem, but I don't know how to find these two constant from a certain function $f(x,y) = u(x,y)+i v(x,y)$.
Is anyone could help me?

This Result and Cauchy Riemann Equations shows that $u(x,y)$ is real part of holomorphic function iff $u$ is harmonic.
So,$u_{xx}+u_{yy}=0$ i.e. $b=-a$. QED
