Complex Functions

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

Complex function mapping

Here:

z,w \in \mathbb{C}

Here:

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.

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November 3, 2026 1 min read

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