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Complex plane

Table of contents: Main regions - Disks - Bernstein ellipses

Main regions

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C={x+yi:xRandyR}\mathbb{C} = \left\{ x + y i : x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \right\}
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Symbol: HH H\mathbb{H} Upper complex half-plane
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H={τ:τCandIm ⁣(τ)>0}\mathbb{H} = \left\{ \tau : \tau \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(\tau\right) > 0 \right\}
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T={z:zCandz=1}\mathbb{T} = \left\{ z : z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| = 1 \right\}
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T={eiθ:θ[0,2π)}\mathbb{T} = \left\{ {e}^{i \theta} : \theta \in \left[0, 2 \pi\right) \right\}

Disks

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

Bernstein ellipses

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Eρ={ρeiθ+ρ1eiθ2:θ[0,2π)}\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.

2019-09-19 20:12:49.583742 UTC