Possibly Difficult Graphing Problem

Tesla23

Joined May 10, 2009
542
Hello,

Yes, but you basically just said exactly what you said in your first post. What you might do is show the relationship between the exponentials and how you got them from the final 'circle'. This is for the benefit of another reader too :)
Thanks much.

Side note: The resulting graph looks like a cardioid, but i dont think it is one unless we stretch the definition a little. A test might help, but i'll leave that for later.
You weren't clear which two equations you didn't understand.

A parametric form of the circle |z|=1 is
\(z=e^{j\theta}

0 \le \theta \le 2\pi\)

so a parametric form for your w curve is

\(w=(e^{j\theta}-1)^2-1

0 \le \theta \le 2\pi\)

I wouldn't have given the complete answer if I'd known it was homework.
 

naickej4

Joined Jul 12, 2015
206
Wait a minute!

http://forum.allaboutcircuits.com/threads/image-drawing-complex-analysis.125175/#post-1012381

You mean you've been tricking us into working someone's homework for them?!

I really expected better from you.
Hi WBahn, I asked MR AI for help on how to solve this with all my working and because I was afraid to post on this forum because I was scared to get "insulted" if i made mistakes. MR AI also posted this for me. Its not his fault just mine.
thanks,sorry for the inconvenience to all if I caused any.
 

WBahn

Joined Mar 31, 2012
29,976
Hi WBahn, I asked MR AI for help on how to solve this with all my working and because I was afraid to post on this forum because I was scared to get "insulted" if i made mistakes. MR AI also posted this for me. Its not his fault just mine.
thanks,sorry for the inconvenience to all if I caused any.
MrAl knows that the policy here is that we don't just work homework problems. That we expect the student to show their work so that it can be reviewed and we can try to identify where the student went wrong and then try to help them overcome the cause for making the error. At the very least, it should have been identified as a homework problem that someone else was working on. Personally, I would have asked that he get your best attempt from you and post in on your behalf. That's not a very efficient way of exchanging attempts and assistance, but if that is what it would have taken for you to not be concerned about being insulted, then that's better than nothing. Instead, it was presented as a problem that HE was asked and strongly implied that he already had worked out the solution and was asking if anyone had any better ones. Well, now it looks very much like that was pure bull and he just wanted to use the fact that we know he is not a student in order to trick us into working the problem in all its gory detail.
 

naickej4

Joined Jul 12, 2015
206
MrAl knows that the policy here is that we don't just work homework problems. That we expect the student to show their work so that it can be reviewed and we can try to identify where the student went wrong and then try to help them overcome the cause for making the error. At the very least, it should have been identified as a homework problem that someone else was working on. Personally, I would have asked that he get your best attempt from you and post in on your behalf. That's not a very efficient way of exchanging attempts and assistance, but if that is what it would have taken for you to not be concerned about being insulted, then that's better than nothing. Instead, it was presented as a problem that HE was asked and strongly implied that he already had worked out the solution and was asking if anyone had any better ones. Well, now it looks very much like that was pure bull and he just wanted to use the fact that we know he is not a student in order to trick us into working the problem in all its gory detail.
Hi Sir, this is the truth I promise you. I can show you all my working and evidence that I worked out which I did provide to him and my many failed attempts. Please I don't want any one to get into trouble.
 

WBahn

Joined Mar 31, 2012
29,976
I saw that you posted work over in the other thread. I would much rather have helped you figure out where you were going wrong (if you even were going wrong) and help YOU move toward a solution that you could own and completely understand so that you could take a clean sheet of paper, work it out on your own with that new understanding, and turn something in that reflected YOUR understanding of the problem and how to work it. Now you have MY solution (and possibly others) that you can copy and turn in and get credit for whether it reflects YOUR understanding or not. I'm hoping that you won't do that, but I have no way to prevent it at this point.

I'm hoping that, in the future, you will be willing to post your problems and your attempts here directly. As long as you are putting forth an honest effort, I don't think you will be treated too harshly by anyone no matter how far off you happen to be. People that refuse to show their work and want the answers just given to them tend to lose the benefit of the doubt pretty quickly and can get mauled pretty severely, but I don't think you will fall into that category.
 

naickej4

Joined Jul 12, 2015
206
I saw that you posted work over in the other thread. I would much rather have helped you figure out where you were going wrong (if you even were going wrong) and help YOU move toward a solution that you could own and completely understand so that you could take a clean sheet of paper, work it out on your own with that new understanding, and turn something in that reflected YOUR understanding of the problem and how to work it. Now you have MY solution (and possibly others) that you can copy and turn in and get credit for whether it reflects YOUR understanding or not. I'm hoping that you won't do that, but I have no way to prevent it at this point.

I'm hoping that, in the future, you will be willing to post your problems and your attempts here directly. As long as you are putting forth an honest effort, I don't think you will be treated too harshly by anyone no matter how far off you happen to be. People that refuse to show their work and want the answers just given to them tend to lose the benefit of the doubt pretty quickly and can get mauled pretty severely, but I don't think you will fall into that category.
No Sir I am not going to copy these answers!!! I will never do that because in 2 months we write an exam on Complex analysis and Laplace transforms, Sequences and Series and Z-transforms. if I just copy the answers I am fooling myself, Thanks for understanding I will attach my working below if you still want me to and next time I will post directly even if my answers seem stupid from logical sense. MR AI told me about the newton method to solve this and he is going to come back to me on that. I am searching the newton method now as we speak. I also was researching Telesa23 way and your way on parametric plots. Its very interesting to know the many ways to solve this. I need to understand all this stuff and more in 2 months because of this major exam. I do distant studies (due to work situation) so no lectures. This forum helped me a lot and I passed Circuit Analysis due to this forum and tips and advice from MR AI.
Also can you explain to me from the same question what if the circle was not x^2 + y^2 = 1
what if the radius was bigger or smaller say? x^2 + y^2 = 4
or x^2 + y^2 = 1/4
how will this affect the image formation???
thank you all.
 

WBahn

Joined Mar 31, 2012
29,976
Also can you explain to me from the same question what if the circle was not x^2 + y^2 = 1
what if the radius was bigger or smaller say? x^2 + y^2 = 4
or x^2 + y^2 = 1/4
how will this affect the image formation???
thank you all.
It's hard (for me) to say. I haven't done much in the way of considering how changing parameters affects graphical plots since high school (more than three decades ago) so it is hard for me to think in terms of those kinds of relationships. The equation for the circle entered my work in two places, so it's really hard for me to guess what the impact would be. How you would answer that question would be to go back and rederive the relationships but using a parameter, R, for the radius and see how it tracks through the equations. Then you are in a position to either consider what effect changing R would have or to simply plot the results for several different values of R and see what the effect is (and then, armed with that knowledge, see if you can understand, from the equations, how changing R ends up having the observed effect).
 

naickej4

Joined Jul 12, 2015
206
he equation for t
he equation for
It's hard (for me) to say. I haven't done much in the way of considering how changing parameters affects graphical plots since high school (more than three decades ago) so it is hard for me to think in terms of those kinds of relationships. The equation for the circle entered my work in two places, so it's really hard for me to guess what the impact would be. How you would answer that question would be to go back and rederive the relationships but using a parameter, R, for the radius and see how it tracks through the equations. Then you are in a position to either consider what effect changing R would have or to simply plot the results for several different values of R and see what the effect is (and then, armed with that knowledge, see if you can understand, from the equations, how changing R ends up having the observed effect).
Awesome thanks Sir, from the way you did it early where you solved by making y the subject of the formula where the radius was 1

I am going to try and solve the equation and make the radius 4 (2^2) and see if the image becomes bigger.

I what to see this relationship for my own knowledge for future reference.

Also what software should I use to plot this?. I did tell MR AI i have Matlab 6.5 but i don't have vast knowledge on plotting graphs

thank you.
 

WBahn

Joined Mar 31, 2012
29,976
I used Excel just because it is easy for me to use (and I use it frequently enough that I don't forget how to use it, which is a big problem for me with packages like Matlab). I don't presently have Matlab, but that would be a good choice. If you don't have much experience with making plots, then this is a good time to get some. Play with it and learn how to do different things with it. The basic plots in Matlab (where you let it choose all the options for you) don't look all that great (to my eye), but with a little bit of research you will learn how to exercise quite a bit of control over them and can get them looking pretty good. Like many software tools, if you spend a LOT of time figuring out how to use it, you can get AMAZING results.
 

naickej4

Joined Jul 12, 2015
206
I used Excel just because it is easy for me to use (and I use it frequently enough that I don't forget how to use it, which is a big problem for me with packages like Matlab). I don't presently have Matlab, but that would be a good choice. If you don't have much experience with making plots, then this is a good time to get some. Play with it and learn how to do different things with it. The basic plots in Matlab (where you let it choose all the options for you) don't look all that great (to my eye), but with a little bit of research you will learn how to exercise quite a bit of control over them and can get them looking pretty good. Like many software tools, if you spend a LOT of time figuring out how to use it, you can get AMAZING results.
Hi Sir, Thank you I will try it out and try to plot this out.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,389
Wait a minute!

http://forum.allaboutcircuits.com/threads/image-drawing-complex-analysis.125175/#post-1012381

You mean you've been tricking us into working someone's homework for them?!

I really expected better from you.

Hello again,

Thanks for looking at the problem.
I think you jump to conclusions too easy, too fast.
Think about what other possibilities there might be besides 'tricking' someone into doing someone else's homework.
1. Did i know it was homework to begin with? Did the user tell me that info?
2. Is it really homework? Did the user post in the homework section when it's just really a problem they wanted to solve to get better in the subject area?

This particular user is very interested in this subject area, and as far as i know will be asking questions a lot in various forums to get better at it in order to meet the degree requirements at a later date.

So you should feel happy that you helped someone :)

Oh i almost forgot, he actually did post his first attempt at solving this and i was very impressed with his work, very neat, well organized, better than any i've seen here from users that want help, even with homework, and if you look at it you'll see it was a very very good attempt at solving this, and due to the complexity i jumped right in.
So i dont think we handled this too badly, given all the facts.
Also, we got three different solutions out of this too now, which means we showed three different ways to do this problem :)
That's great i think.

There is one more little thing we can do if anyone wants to take the time. That is, show why his original solution did not work, unless it really does work. When i tried to use his solution i made some other mistakes in the program i was using (ha ha) so it looked like it did not work, but maybe it does.
What it looks like is that his solution only provides a single point solution, which is not correct of course, but like i said i could have made a mistake.
So we could either show that his solution did work, if reduced more, or that it does not work. But if it does not work, WHY it does not work.
If you care to take a stab at that, but it's up to you, i know we spent a lot of time on this already.
 
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WBahn

Joined Mar 31, 2012
29,976
Hello again,

Thanks for looking at the problem.
I think you jump to conclusions too easy, too fast.
Think about what other possibilities there might be besides 'tricking' someone into doing someone else's homework.
1. Did i know it was homework to begin with? Did the user tell me that info?
2. Is it really homework? Did the user post in the homework section when it's just really a problem they wanted to solve to get better in the subject area?
So I'm jumping to conclusions that something is homework when the very first sentence of the post is, "Please can you help me with my assignment question."?

Really?

But I'll give you the benefit of the doubt when you say that you didn't know it was homework at the time you made your post. But why wouldn't you post YOUR solution so that IT could be discussed?

Oh i almost forgot, he actually did post his first attempt at solving this and i was very impressed with his work, very neat, well organized, better than any i've seen here from users that want help, even with homework, and if you look at it you'll see it was a very very good attempt at solving this, and due to the complexity i jumped right in.
You "jumped right in" because his the first attempt in his post was so good? Yet you started this thread nearly three hours before he started his?
 
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Thread Starter

MrAl

Joined Jun 17, 2014
11,389
Hi,

Well whatever happened maybe i jumped to conclusions too :)
Not entirely sure what you are saying there, but we know what is what now, and future questions may be homework so we'll be more careful.

In any case, it's not the end of the world. I know he is a good student and understands completely the problems associated with not being to understand the subject material. That led me to not be as concerned as i would have been had it been a random posting like we usually see.
If you check over his work, you'll see it is very clear and concise, which tells me this is a student that is really bent on succeeding in his field. I think you'll agree on this.

However, a lesson taught is a lesson learned, and i will try to be more careful in the future.

I can post both my solutions i guess, the first one is more complicated though, the second one easier to understand. I'll dig them up again if you want to take a look.
I did get diverted a little to though, i must admit, because i saw the original solution first and just took off with it. This led to an over complicated solution which you will see.

Take care for now,
Al
 

WBahn

Joined Mar 31, 2012
29,976
What was the original solution you are referring to?

It might be interesting to see both that and your solutions.

I will try to take a look at his original work and comment on it.

And I agree that I think he is a diligent student trying to truly understand what he is studying, which is quite refreshing.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,389
You "jumped right in" because his the first attempt in his post was so good? Yet you started this thread nearly three hours before he started his?
Hi again,

Oh i see what happened now...

You saw that his post came after mine, so you had a question of how i could know it was such a good solution. The answer is that i had previous knowledge of the problem though the PM system. We discussed this a few times and i started to get a little frustrated myself due to the route i took to solve it and also because i made a mistake in a program i wrote to solve it (yikes, ha ha). So i was hoping to see other solutions myself so i posted it.

Yes you'll see he is a very intelligent and responsible individual, which i know from talking to him back and forth for a few days now. So i guess you could say that i had a lot of faith in his integrity when it comes to these assignments. I guess it could have been actual homework though, but he did make a really good attempt in my view, with all the algebra done really well.

But also try to keep in mind that i always have the best interest in mind for students and general visitors to the forums, and if i make a mistake in judgement it's an honest one, as i would never try to deceive someone into doing someone else's homework on purpose. That i think is the worst possible view of what could have happened here.

Ok i'll dig up my solution and post it hopefully a little later today, as soon as possible.
It's interesting but i wont put forth that it is the best solution. I would say yours is the best solution so far, and Tesla's is interesting too but maybe a little too advanced for this, but still better than mine :)
 

naickej4

Joined Jul 12, 2015
206
Hi WBahn and Mr AI, thank you sir. I am trying
What was the original solution you are referring to?

It might be interesting to see both that and your solutions.

I will try to take a look at his original work and comment on it.

And I agree that I think he is a diligent student trying to truly understand what he is studying, which is quite refreshing.
Hi WBahn and Mr AI, thank you sir for the compliments. I am trying my best to understand these advanced engineering topics in mathematics I have no lectures and study distant because I also work. I am not complaining but This Forum/Youtube and self study are my only means of studying. This Forum and advice from MR AI helped me through Circuit analysis last semester so I am sure it will help me with DSP and Maths. I found a good book called advanced engineering mathematics with matlab by Dean Duffy and advanced engineering maths by KA stroud.
here are my solutions that I have provided to MR AI. The solution containing the B is when I tried to simplify and I made a huge mess of it. please find the attached.
 

Attachments

Thread Starter

MrAl

Joined Jun 17, 2014
11,389
What was the original solution you are referring to?

It might be interesting to see both that and your solutions.

I will try to take a look at his original work and comment on it.

And I agree that I think he is a diligent student trying to truly understand what he is studying, which is quite refreshing.

Hello again,

Ok he posted his first try as "question 1" pdf file.

My solution involves looking at the graph of the result and realizing that it is not a function of 'u', but if we split the graph into two parts, we can make two analytical functions of 'u' and then it graphs directly from 'u' as the independent variable.
The place it ended up getting split at was of course these two parts (and looking at the upper half first):
1. For u=-1, to something just over that (the point to the farthest point on the left wing of the graph).
2. For u= that point, to u=3.
So we get two functions:
[1] v=sqrt(-(2*sqrt(2*u+3)+u^2-3))
and:
[2] v=sqrt(2*sqrt(2*u+3)-u^2+3)

Note from here we can either:
1. Graph both functions at once, and reject any imaginary solutions, or
2. Solve for u for the point of separation, then graph one at a time.

Either way the graph looks like the upper half of the graphs shown so far, and the bottom half is of course the negative of those two. So it's really four functions. The top half looks like a sort of snail shell.

What happened originally was i saw the graph posted in "question 1" and so i thought this was wrong. But i like the other solutions too so i am glad this happened :)

That solution is rather difficult to arrive at too, but if you care to try to duplicate it that's up to you as you may find a simpler way. What is interesting about this solution is that the two functions trickle out of the process of somewhat direct algebraic manipulation.

Note there could be a small part of the graph missing here too just after the point of separation. I didnt look too hard for that yet, as it may be another function that needs to be included. What probably happened is that i rejected one or more solutions too early in the process and thus threw out one or more functions needed to describe the complete curve.
LATER: I think i see what happened here, originally it looked like part of the graph was missing,but it's just that it is hard to plot because it requires a very very very small increment in 'u' to see those parts. So it should be complete with just those two functions, and of course making them both negative means there are really four functions.
:)
 
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