It is easy enough to make any given function complex by fixing the domain to some complex region and "seeing what happens". Let us break this down even further:[br][br]Let z be a complex number of the form:[br] [img]https://latex.codecogs.com/gif.latex?z%3Dx+y*i[/img][i], [/i]where [img]https://latex.codecogs.com/gif.latex?x%2Cy%5Cepsilon%20%5Cmathbb%7BR%7D[/img][br]We can view x as the real component and y as the imaginary component of the complex number z. We are not done yet though.[br][br]Let u,v take values for x,y and return another real value such that:[br] [img]https://latex.codecogs.com/gif.latex?u%2Cv%3A%5Cmathbb%7BR%7D%5E2%5Crightarrow%20%5Cmathbb%7BR%7D[/img][br]where f can then be written with the form:[br] [img]https://latex.codecogs.com/gif.latex?f%28z%29%3Df%28x%2Cy%29%3Du%28x%2Cy%29+v%28x%2Cy%29*i[/img][br]Now we have a general equation for Complex Functions and can start talking about differentiation of f.[br][br][br]