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### 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 ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 $|z|<1$?
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)? ...
88 views

Consider ...
64 views

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

I define a function called VoutCoin: ...
44 views

### paraconjugate of polynomial

I'm trying to obtain the paraconjugate of a polynomial with the following code, ...
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} } ...
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'...
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 ...
91 views

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

Suppose the function ...
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]) ...
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^(...
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 ...
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. ...
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 ...
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. ...
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 ...
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 ...
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 ...
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))^(1/3) // N which returns only: 0.601656 + 1....
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### 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 ...
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. ...
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 ...
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 ...
133 views

### Performance of Apart with complex numbers

Consider the following code ...
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 ...
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 ...
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 ...
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:= Chop[10.^-12 + 2. I] Out= 0. + 2. I Why does ...
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 ...
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 ...
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, ...
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 ...
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 ...
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-...
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 ...
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 <...