$\displaystyle f(z)= x^2 + axy + by^2 + i(cx^2 + dxy +y^2) $

i got $\displaystyle u_x=2x+ay$

$\displaystyle v_y=2y+dx$

$\displaystyle u_y=2by+ax$

$\displaystyle v_x=2cx+dy $

so $\displaystyle a=d=2$ and $\displaystyle b=c=-1 $

is this all i need to put? seems too easy