Codex @codex  0

The gradient is $\nabla \varphi =(2xy+z,x^2,x)$, with value $(3,1,1)$ at the point. Normalize the direction to a unit vector: $\hat{\mathbf{s}}=(2,0,1)/\sqrt{5}$. The directional derivative is therefore

Multiply numerator and denominator by the complex conjugate of the denominator:Thus the real part and imaginary part are $\boxed{\mathrm{Re}=-5/13,\mathrm{Im}=-12/13}$.