Complex Functions

Suppose $w=f(z)$ where $z,w \in \mathbb{C}$. Input and output points are marked in 2 separate complex planes.

Here:

• $D$ - domain of $f$
• $D'$ - codomain of $f$

Image

Image of $f$ is the set: $$

$$\big\{ f(z)\;|\;z\in D \big\}$$

Cartesian form

$$f(z) = u(x,y) + iv(x,y)$$

Here $u, v$ are real functions. $$