Finite difference approximations of first order derivatives of complex-valued functions

In this study, we generalize the well-known finite difference method to compute derivatives of a real-valued function to approximate complex derivatives wz and wz for complex-valued function w. Exploring different combinations of terms, we derive several approximations to compute the first order derivatives of complex-valued function. The first, second, third and fourth order of accuracy finite differences to calculate derivatives are studied. Error analysis in test examples are carried out by using Matlab program.