# Help with Complex Polynomial equation in mathematica

• Mathematica
• Don Diego
In summary: I have looked through the documentation, and I can't seem to find ComplexExpand or Simplify. What should I do?I think you should look up "simplify" or "expand" in the help.

#### Don Diego

Hi everybody:
I'm trying to analyse equations of analogue electronic filters, but i can't get the "norm" of the complex polynom if i use variables (or symbols? what's the difference?), here's the simplest exemple (RC low pass filter, a represents R*C*w, reals variables > 0):

Assuming[ a \[Element] Reals && a > 0, Norm[1/(1 + a \[ImaginaryJ])]]

Norm[1/(1 + I a)]

Norm[1/(1 + I a)] ----- the same thing!

Re[] and Im[] doesn't work either!
I will like to uses to find the argument (Arg[] doesn't work)

and after all, make my bode plots!
Thanks

up?? somebody?? help!

Norm? Do you mean Abs?

If you want it to try and simplify things, or expand a function, or other stuff, you should invoke the appropriate functions...

And if you want to plot something, just plot it. If it evaluates to a real number, it doesn't matter what the symbolic form is.

Hi Hurkyl, and thanks for the answer:

My problem is that i can't get the "modulus" or "norm" of the Complex number, once i get the norm (norm = abs) i would like to plot it as a fonction of "w", how can i get the Norm of à complex number without fixed values??
exemple:
Norm[1/(1 + 3 \[ImaginaryJ])]
then i get :
1/Sqrt[10]

with Norm[(1/(1 + a \[ImaginaryJ]))
i get Norm[(1/(1 + a \[ImaginaryJ])), the same thing!

i should get : 1/(\[Sqrt]1 + a^2)
... what ca i do?

What part of my response didn't you understand?

Yeah, it's a drag…
For your particular example, this gives the appropriate result :

http://img185.imageshack.us/img185/319/picture1qs.jpg [Broken]

I suggest you define a function which does the above

Last edited by a moderator:
GREAT GREAT! I'm going to try this! Thanks so much gueromm00! you are great!
I'm going to put my results with à more complex filter!
:):):)! thanks!

Voila Voila!
RLC Low pass filter in the attachement!
thanks a lot!

#### Attachments

• RLC Mathematica.jpg
42.2 KB · Views: 512
Why are you bothering trying to coerce Mathematica to express it in a particular symbolic form when all you really want to do is plot it?

Hurkyl said:
Why are you bothering trying to coerce Mathematica to express it in a particular symbolic form when all you really want to do is plot it?

Well, in my case at least, when simply using the Abs[] function Mathematica hangs when trying to plot…
So, it does make sense to help him a little
I think it is because of the Manipulate[]… (otherwise, I agree with you : since all plots functions have an HoldAll attribute, it doesn't matter what symbolic form its argument evaluates to)

Last edited:
This was just un exemple, what i really want to do it's to manipulate the complex expressions in a theorycal way, I'm learning about filters ok?, i don't want to just plot something without understanding the original relation. my problem was just about the manipulation of complex equations and now it's OK.
Thanks guerom00, you're really nice!

That's fair. It's hard for me to tell, since you didn't really respond to any of my earlier comments.

I am mildly surprised that you cannot just FullSimplify your original expression (with an assuming clause), or possibly ComplexExpand it. Or... was that just not tried? Ah well, I forgot to play with it earlier when I had a chance.

Sorry Hurkyl, but I'm new in mathematica, i didn't know about "complexexpand"... i think that you didn't realize that I'm a newbie, i don't understant everything about mathematica, thanks for yours comments ;)

Hi!
Now i have one new problem, i can't run this Laplace equation (see attachement)

Thanks!

See the "InverseLaplaceTransform" don't show me the answer... why?

#### Attachments

• Laplace problem.jpg
30.9 KB · Views: 507
When I made my reply, I was keying in on your desire to plot, which doesn't require manipulating things into a "nice" form. I was hoping that if you were less interested in plotting and more interested in "simplifying things" or "expand a function"... or that it would prompt you to look up the keywords "simplify" or "expand" in the help.

Have you looked through Mathematica's documentation center? (e.g. under the "help" menu, or by hitting F1 after highlighting a word) It's pretty good. I didn't know about ComplexExpand myself, but I expect it's not hard to find if you started with the page for Expand or Simplify. I think there's even an article on "simplifying functions" but it's been a while since I looked at it.

## 1. What is a complex polynomial equation?

A complex polynomial equation is an algebraic equation that involves variables raised to positive integer powers and constants, with the addition of complex numbers. Complex numbers consist of a real part and an imaginary part, and are written in the form a + bi, where a and b are real numbers and i is the imaginary unit.

## 2. What is Mathematica and how does it help with complex polynomial equations?

Mathematica is a computational software program used for mathematical and scientific computation. It has powerful capabilities for solving complex polynomial equations, including the ability to handle symbolic expressions and work with both real and complex numbers. It also has built-in functions for numerical and analytical solutions, as well as graphing and visualization tools.

## 3. How do I input a complex polynomial equation into Mathematica?

To input a complex polynomial equation into Mathematica, you can use the built-in command "Solve" or "NSolve" followed by the equation and the variables you want to solve for. You can also use the "Expand" function to expand and simplify the equation, if needed. Alternatively, you can use the Wolfram Language to create a polynomial function and then use it to solve for specific values or plot the function.

## 4. Can Mathematica handle higher degree complex polynomial equations?

Yes, Mathematica can handle complex polynomial equations of any degree, including higher degree equations. However, the computation time and memory usage may increase as the degree of the equation increases. It is recommended to use appropriate simplification techniques and optimizations to improve performance.

## 5. How do I interpret the results from Mathematica for a complex polynomial equation?

The results from Mathematica for a complex polynomial equation can be interpreted as the solutions to the equation. These solutions may include real and/or complex numbers, depending on the nature of the equation. Mathematica also provides additional information such as the number of solutions, their multiplicity, and the accuracy of the results.

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