How to plot complex functions on the paper by your hand?
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
asked Dec 28 '13 at 19:45
FreeMind
9071133
|
show 5 more comments
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
asked Dec 28 '13 at 19:45
FreeMind
9071133
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
|
show 5 more comments
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
asked Dec 28 '13 at 19:45
FreeMind
9071133
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
asked Dec 28 '13 at 19:45
FreeMind
9071133
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
asked Dec 28 '13 at 19:45
FreeMind
9071133
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
edited Dec 28 '13 at 19:46
mathematics2x2life
8,05021738
8,05021738
asked Dec 28 '13 at 19:45
FreeMind
9071133
asked Dec 28 '13 at 19:45
FreeMind
9071133
asked Dec 28 '13 at 19:45
FreeMind
9071133
9071133
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
|
show 5 more comments
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
|
show 5 more comments
3 Answers
3
active
oldest
votes
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f620736%2fhow-to-plot-complex-functions-on-the-paper-by-your-hand%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
edited Dec 28 '13 at 19:56
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
answered Dec 28 '13 at 19:50
mathematics2x2life
8,05021738
8,05021738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
add a comment |
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
add a comment |
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5841531
5,5841531
add a comment |
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
answered Jan 22 at 7:03
seaplant
92
answered Jan 22 at 7:03
seaplant
92
answered Jan 22 at 7:03
seaplant
92
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f620736%2fhow-to-plot-complex-functions-on-the-paper-by-your-hand%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53