Okay. A) This just doesn't work. That's a pretty huge problem.

B (probably the answer to the problem))

We know any function on a complex variable can be decomposed:

$\displaystyle f(z) = Re(f(z)) + i[Im(f(z))] = u + iv$

Where u(x,y) and v(x,y) are real-valued functions.

Now, let $\displaystyle g(z) = s + it$ similarly.

Thus, $\displaystyle g(f(z)) = s(u(x,y) + i[v(x,y)]) + i[t(u(x,y) + i[v(x,y)])]$.

so $\displaystyle (g(f(z))' = (s(u(x,y) + i[v(x,y)]))' + (i[t(u(x,y) + i[v(x,y)])])'$

$\displaystyle = s'(u(x,y))u'(x,y) + s'(i[v(x,y)])iv'(x,y) + i[t'(u(x,y))u'(x,y) + t'(i[v(x,y)])iv'(x,y)$

Right? But then what happens to the i's inside the real-valued functions?