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1answer
33 views

Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything

I think it is straightforward from the title, Simplify[Im[1/(x+I)], x > 0] spits out, Im[1/(x+I)] while I would have ...
2
votes
1answer
85 views

Taking real and imaginary parts after reciprocal

I noticed the following strange scenario. When I defined a variable to be real, Mathematica does not only recognize that it is real after taking an inverse. How can I resolve this so that it will ...
0
votes
2answers
80 views

Result with assumptions contradicts previous result

Without assuming anything on the argument of the complex number inside the Gamma function ...
1
vote
1answer
90 views

How to define a complex function with assumptions?

I'm trying to define a complex function to be able to do analytic calculations. Specifically, I want to define a function $A(x,t)$ in the complex plane with argument $\theta(x,t)$ and modulus $R(x,t)&...
2
votes
1answer
65 views

Choose a branch cut using assumptions

I understand Sqrt function won't simplify expressions such as $\sqrt{x^2}$ unless there is an assumption that $x \in \mathbb{R}$. In my computation, I get an output containing an expression like this ...
1
vote
1answer
111 views

Can this integral be calculated using Mathematica?

I have the following integral: $$ \int_{-\infty}^{\infty} \frac{\mathrm d\tau}{2\pi \mathrm i} \int_{-\infty}^{\infty} \frac{\mathrm d\tau'}{2\pi \mathrm i} \frac{\mathrm e^{-c^2(\tau - \tau')^2}}{(\...
1
vote
4answers
71 views

Problem with particular simplification of complex function under assumptions

I have proven that $expr=(1 - i)(\dfrac{1+z}{1-z})^{1/4}\dfrac{\sqrt{ 1-z^2+i z\sqrt{1 - z^2}}}{1+z-i\sqrt{1 - z^2}}=1$ when it is assumed that $z\in R$ and $|z|<1$ and when I also plot the real ...
0
votes
1answer
74 views

Finding the real part of a complicated complex expression

I've the following code: ...
3
votes
1answer
79 views

Complex Conjugate with Refine

I am trying to do symbolic manipulations in MMA and I need it to take a complex conjugate of functions with real arguments, like: ...
0
votes
0answers
50 views

Using Refine function and take real part of a symbolic expression

I am trying to take the real part of the a complex expression using Refine function. However, the result doesn't come out as expected. The final result still ...
1
vote
1answer
69 views

Trouble getting Mathematica to assume some parameters are real and simplify the expression [duplicate]

Say I enter the following code: FullSimplify[Im[r*Exp[I*theta]^2 + (s + I*t)*Exp[I*theta]], Element[theta | r | s | t, Reals]] I expect to get: ...
1
vote
1answer
72 views

Simplifying a complex function with assumptions

By experiments, I am expecting that the following complex function ...
2
votes
1answer
43 views

Verifying $F(A)\subset B$ numerically and symbolically for a complex function $F$ with assumptions

As it is mentioned in a previous question of mine, one can construct a holomorphic bijection between the (open) unit disc $D=\{z\in{\bf C}: |z|<1\}$, and a domain $D\setminus\overline{B_{1/2}(-1/2)}...
3
votes
2answers
124 views

Series default assumptions?

I have a question about the "Series" command. Specifically, the following input Series[Sqrt[x^2], {x, 0, 2}] gives me the following output ...
0
votes
0answers
34 views

Assuming and Conjugate do not work as expected [duplicate]

I tried to work with Conjugates in Mathematica and it did not produce my desired result. I learned about assumptions and figured they're my way to go. This is the code: ...
4
votes
0answers
119 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
3
votes
1answer
239 views

Why doesn't a real variable's conjugate evaluate to itself?

I have this code (it's just a snippet to exemplify my issue): Assuming[Element[a, Reals],Conjugate[a]] Which results in the output: ...
9
votes
2answers
170 views

Problem with Identifying Complex Components

I am trying to isolate out the real and complex terms in a fairly large expression. During the process, I have made several assumptions that last throughout the entire process. ...
2
votes
1answer
180 views

Mathematica does not distribute conjugation when used with Assuming sometimes?

If I input: Assuming[$x_{-} \in$ Reals, FullSimplify[Conjugate[$e^{i x_1}x_2$]]] Then the output is: $e^{-ix_1}x_2$ As it should be. And if instead I do: Assuming[$x_{-} \in$ Reals, FullSimplify[...
3
votes
2answers
475 views

Simplifying expressions with Abs

I have a long expression which seems really complicated due to some Abs[] terms that should be simplified. However, even with the right assumptions, the expression ...
0
votes
1answer
290 views

How do I declare that a variable represents a real number? [duplicate]

How do I tell Mathematica that a variable is a real number. I searched for this question here and in Google and nothing that was suggested seems to work for me. I must be missing something. My code is ...
0
votes
1answer
383 views

Simplifying complex expressions

I'm trying to work with complexes and I want Mathematica to know that all variables are real unless I explicitly assigned the variable with an I so I wrote: ...
4
votes
3answers
2k views

Conjugating symbolic expression [duplicate]

I am trying to conjugate a symbolic expression, and I have explicitly stated the real terms. However, I simply can't get it to work: ...
6
votes
2answers
586 views

Simplify — is this simplest result Mathematica can provide? [duplicate]

I have a question about Simplify: When I do a simplification the returned result is not as simple as I want. When I ask for the Norm of an complex expression, ...
4
votes
4answers
7k views

How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
0
votes
1answer
191 views

Simplifying Complex Numbers that contain physical units

I am trying to evaluate the following: Simplify[Meter Nano Re[(a + I b)/(Meter Nano)], Assumptions -> Element[{a, b}, Reals]] However, Mathematica returns: <...
13
votes
3answers
7k views

Complex number operations: telling Mathematica variables are real

I want to do Conjugate[a + b*I], but when I do that, the solution is Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
9
votes
1answer
3k views

Is it possible to set a variable as a positive one in the whole notebook?

I'm having issues during integration due to the fact that Mathematica doesn't know if an undefined variable is positive or not (it gives me complexes which bothers me in the end). For example I do ...
6
votes
1answer
978 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
19
votes
2answers
1k views

Why doesn't FullSimplify drop the Re function from an expression known to be real?

For some reason Mathematica does not properly simplify this expression: ...
15
votes
2answers
15k views

How to specify assumptions before evaluation?

If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example : ...