# Complex plane

## Main regions

$\mathbb{C} = \left\{ x + y i : x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \right\}$
Symbol: HH $\mathbb{H}$ Upper complex half-plane
$\mathbb{H} = \left\{ \tau : \tau \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}(\tau) > 0 \right\}$
$\mathbb{T} = \left\{ z : z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| = 1 \right\}$
$\mathbb{T} = \left\{ {e}^{i \theta} : \theta \in \left[0, 2 \pi\right) \right\}$

## Disks

$\operatorname{OpenDisk}\!\left(z, r\right) = \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z - t\right| < r \right\}$
$\operatorname{ClosedDisk}\!\left(z, r\right) = \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z - t\right| \le r \right\}$

## Bernstein ellipses

$\mathcal{E}_{\rho} = \left\{ \frac{\rho {e}^{i \theta} + {\rho}^{-1} {e}^{-i \theta}}{2} : \theta \in \left[0, 2 \pi\right) \right\}$

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC