KnowraComplex derivativeLinked fromLinked fromThe 8 pages that link to Complex derivative, each with the reason it gives.All 8Related 7Narrower topic 1Identity theoremRelated: Complex differentiability throughout an open domain makes the functions holomorphic.Conformal mapRelated: A nonzero derivative acts locally as a rotation and scaling, preserving angles.Cauchy–Riemann equationsRelated: The equations ensure directional difference quotients agree under the stated smoothness condition.Schwarz lemmaRelated: The theorem bounds the derivative magnitude at the fixed point.Complex differentiabilityRelated: It is the value produced by complex differentiability at a point.Bloch's theorem (complex analysis)Related: Derivative size is central to obtaining a nontrivial image disk.Analyticity of holomorphic functionsRelated: A single complex derivative requires compatible behavior from every direction in the plane.