# unit disk

The unit disk in the complex plane, denoted $\Delta$, is defined as $\{z\in{\mathbb{C}}:|z|<1\}$. The unit circle, denoted $\partial\Delta$ or $S^{1}$ is the boundary $\{z\in{\mathbb{C}}:|z|=1\}$ of the unit disk $\Delta$. Every element $z\in\partial\Delta$ can be written as $z=e^{i\theta}$ for some real value of $\theta$.

 Title unit disk Canonical name UnitDisk Date of creation 2013-03-22 13:37:45 Last modified on 2013-03-22 13:37:45 Owner brianbirgen (2180) Last modified by brianbirgen (2180) Numerical id 8 Author brianbirgen (2180) Entry type Definition Classification msc 30A99 Synonym unit disc Related topic ConformalMobiusCircleMapTheorem Related topic SchwarzLemma Related topic Complex Related topic UpperHalfPlane Related topic UnitDiskUpperHalfPlaneConformalEquivalenceTheorem Related topic UnitDisc2 Defines unit circle