# Definition:Holomorphic Function/Complex Plane

## Definition

Let $U\subset\C$ be an open set.

Let $f : U \to \C$ be a complex function.

Then $f$ is **holomorphic in $U$** if and only if $f$ is differentiable at each point of $U$.

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Let $U\subset\C$ be an open set.

Let $f : U \to \C$ be a complex function.

Then $f$ is **holomorphic in $U$** if and only if $f$ is differentiable at each point of $U$.

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