Kompleksinen kuvaus
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Jos kompleksimuuttujan kompleksiarvoinen funktio f:C→C on derivoituva ja f′(z0)≠0, niin funktio f säilyttää kulmien suuruuden pisteessä z0.
Tästä johtuen derivoituvat kompleksifunktiot "venyttävät ja kiertävät, mutta eivät vääristä muuten".
Derivoituvilla kompleksifunktioilla on paljon mielenkiintoisia ominaisuuksia ja ne ovat hyödyllisiä myös luonnonilmiöitä tarkastellessa.