# Definition
A [[Complex Functions|complex function]] $f(z)$ 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|differentiable]], we should expect **relations** between $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$.