unit diskUnitDisk2003-05-12 11:43:022003-05-13 15:02:14Definitionunit circle% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amsmath}
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% define commands hereThe 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 $\theta$.