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0
votes
1answer
49 views

Finding the negative real root of in set of solutions under a varying constraint

Suppose I have a function and its derivative like: V = x^3.5 - x*y Vx = D[V, x] I first solve V for ...
1
vote
1answer
71 views

Plotting $f: x + i\,y \mapsto u + i\, v$ with Plot3D and mapping $v$ to color

Mathematica already has ComplexPlot3D that plots ReIm[x, y] against Abs[f(z)] and ...
12
votes
3answers
429 views

Finding and visualization of branch cuts and branch points

Is it possible to determine branch cuts and branch points for complicated functions using mathematica Iam trying to determine the brnach cuts and branch points of this complicated function We have ...
0
votes
2answers
76 views

Problem in dealing with Sign function

Let my function be $f(x)=e^{|x|}$. I wish to find $f''(x)$, this can be done as- $f'(x)=$sgn$(x)e^{|x|}$ $f''(x)=$sgn$(x)^2e^{|x|} =e^{|x|}$ In Mathematica, I am trying to plot $f''(x)$, it ...
1
vote
2answers
77 views

Working with complex valued functions

I have a function which has real and imaginary parts and I need to differentiate both parts separately. This is a simpler example of what I have tried, without success: ...
2
votes
1answer
49 views

How to declare derivatives of a multivariable function as real in order to get Re and Im part of the expression?

Re and Im work properly, with appropriate assumptions, in the example like this ...
0
votes
0answers
21 views

Plotting a function on a complex plane [duplicate]

I am new to Mathematica and I would like to know how to plot a complex function, say $f(z) = \frac{-z}{z^2 - 1}$ for $|z|<1$?
1
vote
2answers
72 views

Finding Imaginary part of a complex function with 2 arguments

How to make mathematica gives the imaginary part of a certain complex function in the form of trigonometric functions such as sin(s-t) and cos(s-t)? ...
1
vote
1answer
88 views

ComplexExpand does not fully expand

Consider ...
1
vote
1answer
64 views

Magnitude is returning a complex number if I precede it with Complex Expand?

I define a function called VoutCoin: ...
0
votes
0answers
44 views

paraconjugate of polynomial

I'm trying to obtain the paraconjugate of a polynomial with the following code, ...
1
vote
1answer
70 views

Re[“Complex Exponential”] does not return Cosine [closed]

I am having some problems retrieving the real part of a complex function. I have a function which looks as follows: $$ 2^{-\dfrac{4\left( \frac{x}{\sqrt{2}}+\frac{z}{\sqrt{2}} \right)^{2}}{w^2} } ...
2
votes
0answers
23 views

`FunctionDomain` working with real part

Is there any reason why Mathematica evaluates the following FunctionDomain[Re[((I + 1) x)], x] (* False *) as False, where I'...
0
votes
2answers
75 views

Mathematica gives imaginary results for polynomials [duplicate]

I was trying to plot a very simple polynomial function: Plot[x^(2./3.),{x,-0.5,-0.2}] Mathematica tells me that in this region, the result is always imaginary, but from fundamental math the result ...
1
vote
1answer
91 views

The function is real, while its integral is complex [duplicate]

Suppose the function ...
1
vote
1answer
35 views

Strange values and plot of the given function

Suppose the function f[s2_,m_,m2_] = (s2 - m^2 + m2^2 -Sqrt[m^4 - 2m^2(s2+m2^2) + (s2-m2^2)^2])/(s2 - m^2 + m2^2 +Sqrt[m^4 - 2m^2(s2+m2^2) + (s2-m2^2)^2]) ...
-1
votes
1answer
276 views

Evaluate complex exponential expression [closed]

I am trying to evaluate the modulus of the following expression. The expected result is 1.3. However, I tried Abs, ComplexExpand but still couldn't get it. Can anyone help me out? Thanks. 1/(1+e^(...
1
vote
0answers
69 views

Very slow Absolute value computation (Improvement need)?

I have to compute the following absolute value. When computing the absolute value of the two pieces separately, everything works fine. When summing up and then evaluating the Abs of the Sum, the code ...
0
votes
1answer
218 views

Why is Series with Abs giving an imaginary unit as output? [closed]

I have a simple integral of an absolute value. However, the output is showing an imaginary unit. In a previous question I have been told the problem is the Series. ...
0
votes
2answers
434 views

Evaluating Series at a point not working [closed]

I have a series as an output and I am trying to plot it and/or evaluate it. How come that doesn't work? I get: Attempt to evaluate a series at the number 0.10001838571428572`. Returning ...
0
votes
0answers
79 views

Why do I get Imaginary unit after Abs and Complex expand?

I am getting an imaginary unit in the output after Abs and saying Complex Expand, why? Then, when I integrate in x and z, I miss beta. I don't get why beta vanishes in the definite integral. ...
0
votes
2answers
107 views

Power function applied to complex number [closed]

In part of the full form of the Mathematica output, I observe this expression: Power[Complex[1, 1], Rational[2, 3]] But I am not sure how to interpret this: technically, the power function is not a ...
0
votes
1answer
215 views

Extracting the Argument of a Complex Exponential

Let's say I have a complex exponential A*Exp[I*B], and I want to find B. The obvious way is to use the ...
1
vote
1answer
141 views

Wrong behaviour of ComplexExpand and Conjugate

This input gives the wrong result ComplexExpand[Conjugate[f[x]], {x}] (*f[x]*) instead of Conjugate[f[x]]. In particular it ...
0
votes
0answers
55 views

Why the cubic root of negative number returns a complex value only? [duplicate]

I am trying to evaluate the cubic root of a negative number $(5 (7 - 3 \sqrt{6}))^{1/3}$ by (5 (7 - 3 Sqrt[6]))^(1/3) // N which returns only: 0.601656 + 1....
2
votes
2answers
91 views

Pick complexes out from a list

Consider the assumptions $Assumptions = {Element[a,Reals], Element[z,Complexes]} I'm looking for a test, to be applied on a ...
1
vote
0answers
52 views

Different Derivative's output with ComplexExpand

Consider this expression f = Abs[ x + I ] with this assumption $Assumptions = Element[x, Reals] Now there is something ...
1
vote
0answers
43 views

Can you define “| |” to be the same as “Abs[ ]”? [duplicate]

When calculating the modulus of a complex number in Mathematica, the standard (and probably least-ugly) way of doing it is by using the Abs[ ] function. When doing ...
3
votes
1answer
394 views

Reduce a complex inequality

Reduce[Abs[1/(1 + I/Sqrt[α])] < 0.5, {α}] It is taking long time to run. Can any one help me to get the reduced condition in terms of $\alpha$ or its modulus. ...
11
votes
1answer
187 views

Definition of Mod and Quotient with complex arguments

How are Mod and Quotient defined for three real/complex arguments? I wasn't able to find the definition. My main surprise so ...
0
votes
3answers
586 views

Write complex number in terms of absolute value and phase

I have a long vector and some of the values (19 out of 64) are complex. I got them using the Mathematica Rationalize function, so the complex ones are written in the a+bi form. Is there a function I ...
5
votes
1answer
133 views

Performance of Apart with complex numbers

Consider the following code ...
0
votes
0answers
88 views

Using DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
9
votes
1answer
2k views

Branch cuts of sqrt

I was trying to plot some complex functions with branch cuts on mathematica but I have two problems. 1) The function is with z-Sqrt[z-1]*Sqrt[z+1] with z complex. Now Mathematica says that the ...
5
votes
3answers
501 views

How to tell Mathematica to get the real-only inverse function?

The problem I have is that Mathematica seems to play better with complex numbers so that the result of N[InverseFunction[Function[x,x^3]][-1]] is ...
3
votes
1answer
416 views

Why `Chop` does not make the real part of machine complex numbers an exact zero? [duplicate]

The documentation says Chop does not make the real part of machine complex numbers an exact zero: In[2]:= Chop[10.^-12 + 2. I] Out[2]= 0. + 2. I Why does ...
4
votes
2answers
1k views

Derivative of conjugate multivariate function

I have a problem with Mathematica, taking the derivative of the conjugate of some function. I know that a similar question has been posed before here, but the solution did not work for multivariate ...
3
votes
1answer
1k views

Working with derivative of conjugate of a complex number

I have a complex function, lets say $g(x)$. I want to take its and its conjugate's derivative. I need the solution of derivative which must be symbolically and computationally efficient. Lets take an ...
29
votes
3answers
43k views

How to tell Mathematica that certain variables are real/imaginary, integer-valued, etc

I'm trying to expedite some quantum mechanical calculations (expectation values etc.) by running them through Mathematica. When I say, for example, ...
4
votes
1answer
131 views

How to apply RootLocusPlot correctly

I have to analyze the complex regions of variable c which is define obtained with InverseLaplace help in the form ...
0
votes
0answers
306 views

Phase Unwrap List Of Points: Implementing continuous phase/Arg function for List of Points [duplicate]

I am looking for a function to unwrap phase of a list of points as done here for the continuous case. I have the Re/Im data as my input and would like the unwrapped phase as the output. Does anyone ...
1
vote
1answer
2k views

Plotting a complex function [duplicate]

What does it mean if this message appears: {Im[(1-E^Times[<<3>>] f)/(1-Power[<<2>>] f)]-0,Im[(1-E^Times[<<3>>] f)/(1-Power[<<2>>] f)]-0} must be a list of equalities or real-...
16
votes
4answers
3k views

Moving the location of the branch cut in Mathematica

According to the documentation, Mathematica chooses the branch cut for $\log(z)$ to lie along the negative real axis. It it possible to change this so that it lies along the positive axis or elsewhere ...
4
votes
2answers
253 views

How does RootOfUnityQ work?

How does Mathematica's RootOfUnityQ function work? That is, how does Mathematica know if a number is a root of unity? Example: Let $x = \frac{1-i \sqrt{2+\sqrt{5}}}{1+i \sqrt{2+\sqrt{5}}}$. Then <...