File:ComplexEx2.jpg
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Summary
| Description |
English: f=exp(-z^2) in the comples z=x+iy plane. Levels of integer values of Re(f) are shown with thick black lines. Level of Im(f)=0 is shown with think green line.
Negative integer values of Im(f) are shown with thick red lines. Positive integer values of Im(f) are shown with thick blue lines. Intermediate levels of Im(f)=const are shown with thin green lines. Intermediate levels of Re(f)=const are shown with thin red lines for negative values and with thin blue lines for positive values. |
| Date | |
| Source |
 This diagram was created with Mathematica. << Graphics`ImplicitPlot`
RGB[x_, y_, z_] = RGBColor[x, y, z];
u=Re[Exp[-(x+I*y)^2]];
QR=ImplicitPlot[{u==-4,
u==-3, u==-2.8,u==-2.6,u==-2.4,u==-2.2,
u==-2., u==-1.8,u==-1.6,u==-1.4,u==-1.2,
u==-1., u==-0.8,u==-0.6,u==-0.4,u==-0.2,
u==0,u==0.2,u==0.4,u==0.6,u==0.8,
u==1.,u==1.2,u==1.4,u==1.6,u==1.8,
u==2.,u==2.2,u==2.4,u==2.6,u==2.8,
u==3.,u==4.},{x,-3,3},{y,-3,3},PlotPoints->120,
PlotStyle->{{Thickness[.01],RGB[1,0,0]},
Thickness[.01],RGB[1,0,0],RGB[1,0,0],RGB[1,0,0],RGB[1,0,0],
Thickness[.01],RGB[1,0,0],RGB[1,0,0],RGB[1,0,0],RGB[1,0,0],
Thickness[.01],RGB[1,0,0],RGB[1,0,0],RGB[1,0,0],RGB[1,0,0],
{Thickness[.01]},RGB[0,0,1],RGB[0,0,1],RGB[0,0,1],RGB[0,0,1],
{Thickness[.01]},RGB[0,0,1],RGB[0,0,1],RGB[0,0,1],RGB[0,0,1],
{Thickness[.01]},RGB[0,0,1],RGB[0,0,1],RGB[0,0,1],RGB[0,0,1],
{Thickness[.01]},{Thickness[.01]}
}];
u=Im[Exp[-(x+I*y)^2]];
QI=ImplicitPlot[{u==-4,
u==-3, u==-2.8,u==-2.6,u==-2.4,u==-2.2,
u==-2., u==-1.8,u==-1.6,u==-1.4,u==-1.2,
u==-1., u==-0.8,u==-0.6,u==-0.4,u==-0.2,
u==0,u==0.2,u==0.4,u==0.6,u==0.8,
u==1.,u==1.2,u==1.4,u==1.6,u==1.8,
u==2.,u==2.2,u==2.4,u==2.6,u==2.8,
u==3.,u==4.},{x,-3,3},{y,-3,3},PlotPoints->120,
PlotStyle->{{Thickness[.01],RGB[1,0,0]},
{Thickness[.01],RGB[1,0,1]},RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],
{Thickness[.01],RGB[1,0,0]},RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],
{Thickness[.01],RGB[1,0,0]},RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],
{Thickness[.01],RGB[0,1,0]},RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],
{Thickness[.01],RGB[0,0,1]},RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],
{Thickness[.01],RGB[0,0,1]},RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],RGB[0,1,0],
{Thickness[.01],RGB[0,0,1]},{Thickness[.01],RGB[0,0,1]}
}}}];
Show[QR, QI];
|
| Author | Domitori |
| Permission (Reusing this file) |
Use it for free. |
 | This image was uploaded in the JPEG format even though it consists of non-photographic data. This information could be stored more efficiently or accurately in the PNG or SVG format. If possible, please upload a PNG or SVG version of this image without compression artifacts, derived from a non-JPEG source (or with existing artifacts removed). After doing so, please tag the JPEG version with {{Superseded|NewImage.ext}} and remove this tag. This tag should not be applied to photographs or scans. If this image is a diagram or other image suitable for vectorisation, please tag this image with {{Convert to SVG}} instead of {{BadJPEG}}. If not suitable for vectorisation, use {{Convert to PNG}}. For more information, see {{BadJPEG}}. |  |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 05:58, 14 July 2008 | | 288 × 288 (46 KB) | wikimediacommons>Domitori | {{Information |Description={{en|1=f=exp(-z^2) in the comples z=x+iy plane. Levels of integer values of Re(f) are shown with thick black lines. Level of Im(f)=0 is shown with think green line. Negative integer values of Im(f) are shown with thick red lines |
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