I have a complex function as f(x) = g(x) + I h(x). Because f(x) is very complicated function and depend on some parameter. I want to know whether there is a way to prove that g(x) or h(x) is even function or odd function??? I checked numerically, the pictures show that g(x) is even function and h(x) is odd function. Then I guess function h(x) and g(x) has that characters.
I am grateful for any help.