File:Non-holomorphic complex conjugate.svg
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Summary
[edit]DescriptionNon-holomorphic complex conjugate.svg |
English: Diagram showing why the function is not holomorphic. Along the real axis, it is equal to the function g(z) = z, and the limit of the slope as it approaches zero is 1. Along the imaginary axis, it is equal to the function g(z) = -z, and the limit of the slope as it approaches zero is -1. Other angles give yet different limits. Without a single matching limit, the function is not differentiable. Source below. |
Date | |
Source |
Own work This W3C-unspecified diagram was created with Mathematica. |
Author | User:Dcoetzee |
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[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
Source
[edit]Mathematica source:
Show[Plot[{x, -x}, {x, -2, 2}, PlotStyle -> Black], ListPlot[{{1, 0}, {-1, 0}, {0, 1}, {0, -1}, {1, 1}, {-1, -1}, {-1, 1}, {1, -1}}, PlotStyle -> PointSize[Large]], AxesStyle -> FontSize -> 14, AspectRatio -> 1, PlotRange -> {{-2, 2}, {-2, 2}}]
LaTeX source:
$$ \frac{\bar{z} - \bar{0}}{z-0} $$ $$ 1 $$ $$ i $$ $$ -1 $$ $$ -i $$
Converted to SVG using [1] and embedded in the SVG with Inkscape. Axes labels from Mathematica removed in Inkscape.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 02:13, 26 March 2013 | 92 × 139 (65 KB) | Dcoetzee (talk | contribs) | {{Information |Description ={{en|1=Diagram showing why the function <math>f(z) = \zbar</math> is not holomorphic. Along the real axis, it is equal to the function g(z) = z, and the limit of the slope as it approaches zero is 1. Along the imaginary a... |
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