Complex Functions

Complex Functions

$w=f(z)$ with in- and output being Complex Numbers.

Limits

• $lim\_t\to 1(z)=z\_0$ such that $lim\_t\to 1|z(t)-z\_0|=0$
• When $w=f(z)$ , its limit exists at $(x\_0,y\_0)$ when $lim\_(x,y)\to (x\_0,y\_0)(u(x,y))=u\_0$ and $lim\_(x,y)\to (x\_0,y\_0)(v(x,y))=v\_0$ (exist).

Singularities

A singularity refers to a point, $z$, in the complex plane inside an open region $R$ containing $z$ when all other values in $R$ are part of the domain of a complex differentiable function. For Example the point $z=0$ is a singularity of the function $f(z)=\frac{1}{z}$.