Definition

A Complex Functions f(z) can be seen as a function of two real variables. Hence

f(z) = f(x + iy) = f(x, y).

When interpreted appropriately.

[!example] For instance
f(z) = z^2 = (x + iy)^2 = x^2 - y^2 + 2ixy

Suppose f is Differentiable, we should expect relations between \frac{\partial f}{\partial x} and \frac{\partial f}{\partial y}.