"Holomorphicity" refers to the property of a function that is complex differentiable in a region of the complex plane. Some synonyms for this term include: analyticity, complex differentiability, conformal invariance, and regularity. Analyticity refers to the same property of being complex differentiable, but the term is more commonly used in the context of real analysis. Complex differentiability is a more technical term for the same property. Conformal invariance refers to the property of a function that preserves angles, which is a consequence of holomorphicity. Finally, regularity refers to a broader class of properties including continuity, differentiability, and smoothness, of which holomorphicity is a special case.