\[ if: w=w(x,y), and: w=u+iv, then: u==x, v==y, then, w=x+iy (??) \]
\[ \delta w=w(x+\delta x, y+\delta y) - w(x, y)=\delta x +i\delta y \]
\[ \delta z(\partial w/\partial z)+\delta z^*(\partial w/\partial z^*) =\delta (x+iy)* 0.5*(\partial w/\partial x+i*\partial w/\partial y)+\delta (x-iy)*...