If we want to check an integrability of an almost complex structure in $R^{4}$ is it enough to take vectors $X=X^{1}\frac{\partial}{\partial x^{1}}$ and $Y=Y^{1}\frac{\partial}{\partial x^{1}}$ and then calculate Nijenhuis tensor $N(X,Y)$, or we must calculate $N$ on vectors $X=X^{1}\frac{\partial}{\partial x^{1}}+X^{2}\frac{\partial}{\partial x^{2}}+X^{3}\frac{\partial}{\partial y^{1}}+X^{4}\frac{\partial}{\partial y^{2}}$ and $Y=Y^{1}\frac{\partial}{\partial x^{1}}+Y^{2}\frac{\partial}{\partial x^{2}}+Y^{3}\frac{\partial}{\partial y^{1}}+Y^{4}\frac{\partial}{\partial y^{2}}$?
Thank you!