>>19
It is bad because you have not defined derivatives for imaginary numbers. Second you have assumed that d(ln(z))/dx is equal to (dz/dx)/z which you have not yet proven for imaginary numbers. Even more problematic is the fact that you have used the imaginary logarithm which you have not even defined. You could, however, define it to be the imaginary function whose derivative is 1/z for any imaginary number, which is a complex extension of the real logarithm.