Questions tagged [complex]

Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.

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Solving equation for Complex conjugate

How to solve the equation like this: $-par-(x+yi)-a\overline{r}=0 $ where $p,a,x,y$ are constant real numbers, $r$ is complex number and $\overline{r}$ is its complex conjugate. I want to solve for $r$...
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2answers
82 views

Calculating the convergence value of summation

Could you please tell me what value the left side of the inequality converges to? (H and P are constant values greater than 2 and n can go to infinity) $$\sum_{n=1}^...
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0answers
45 views

Specifying Contours in “CyclicReImLogAbs” for ComplexPlot/ComplexPlot3D

How can I specify where and/or how many contours appear in ComplexPlot and ComplexPlot3D when using the "CyclicReImLogAbs" color function? I'm referring specifically to the black and white ...
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1answer
84 views

How to plot Quantum Wave-Funktions like $e^{ix^2}$

I would like to Plot a function like $e^{ix^2}$, similar to the one seen in this video at 1:26: https://www.youtube.com/watch?v=p7bzE1E5PMY&t=86s. I think what I'm trying to do is to plot the ...
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0answers
56 views

Integrating real function gives a complex value

I want to integrate this quite complicated function Sin[2 Pi n x r0/L]*u[x, (m + 1/2) Pi - (nu I Pi/2), kappa I, nu] over x, where ...
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1answer
40 views

Editing complex arrays for export to Python

Quick question, can anyone advise on an efficient way to convert complex arrays with complex part denoted '${I}$' in Mathematica to '$j$' (as used in Python) and curly brackets '{}' replaced with '[]' ...
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1answer
128 views

Analytical Integration

I have a question on analytical integration. z = y/ps; n = 0.95; A1 = Integrate[((a (a + z) - r^2)/r)^0.95 - (n z) ((a (a + z) - r^2)/r)^-0.05, r] Answer: ...
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1answer
56 views

How to plot the solutions of $f(z,a)=0$ for $z$ in the complex plane?

I have an equation $f(z,a)=0$ where $z$ is a complex variable $\frac {56}{10}<z<2\pi$ and $a$ is a real variable $0<a<\pi$. I want to plot solutions of this equation on the complex plane $...
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3answers
78 views

Unwrapping a continuous function given by arg

I want to find the Phase difference from a function like $\arg(f(\infty))-\arg(f(0))$ considering the phase jumps in between. This function is continuous but arg might wrap it around, $[-\pi,\pi[$ is ...
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0answers
34 views

How to write a complex no linear term in loop of a differential equation system?

I have this system of equations $$ i \frac{d \psi_{m}}{dt} = k \psi_{m-1} + k \psi_{m+1} + \gamma \vert \psi_{m} \vert^{2} \psi_{m} $$ and this is my code ...
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38 views

How can I plot complex functions which take small values?

I would like to know, how can I plot some functions that have oscillating behavior each function can be plot independent. The goal is to show both oscillations even is they are very small values. ...
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1answer
54 views

Mathematica returns incorrect evaluation of integral

Consider the integral $$ \begin{equation} u(x):= \lim_{\eta \to 0^+}\int_{-\infty}^\infty \frac{d s}{s^2 + 1} \left( \frac{1}{x - i \eta - \sqrt{s^2 + 1}} - \frac{1}{x - i \eta + \...
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1answer
56 views

Limit of a complex function of a complex variable expressed in polar form

I've got the complex function $$f(t;z,\mu) = \mathrm{e}^{-z\sinh t-\mu t}$$ where $$t=R \mathrm{e}^{i\theta},\theta \in [0,\pi/2]$$ The function depends on two parameters, $$z>0, \mu \in \mathbf{C}$...
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52 views

How to avoid i in roots of cubic

For a general cubic Mathematica applies the formula and the output has i=sqrt(-1) in 2 of the roots. Roots[A*x^3 + B*x^2 + C*x + D == 0, x] I want the roots in a ...
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0answers
50 views

numerical integration of an integral with singularity

I want to compute the following integral numerically in Mathematica, $$ \int_{-\infty}^{\infty} dw' \;\frac{\Gamma(\delta-4iw') 4^{4iw'}}{(i(w'-1)+\epsilon)^{1-4iw'}} $$ where $0<\epsilon, \delta≪1$...
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1answer
256 views

How to recreate this complex iteration

I came across this image in a book Im reading: (taken from Rational Iteration Complex Analytic Dynamical Systems from Steinmetz. I hope it is okay to share it here) and I try to recreate it in ...
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1answer
68 views

My plotting comes out to be gray not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph??h

My graph comes out to be gray, not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph or what I can deduce from ...
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3answers
89 views

Export Long Plot with No Whitespace

Observe the following code: ...
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0answers
34 views

Export 3D Mesh without shading issues

I can export a mesh to a .obj file such as with the following: ...
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1answer
106 views

Why is ComplexPlot So Slow?

I'm plotting the spherical harmonics on $\phi\in(-\pi,+\pi)$ and $x=\cos\theta\in(-1,+1)$, ...
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2answers
73 views
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29 views

Force Mathematica to take real values of cube roots in expressions when simplifying [duplicate]

I am dealing with an algebraic mess of variables for a project and for some reason, even though the function is real, Mathematica had been spitting out imaginary values to me. This issue has been ...
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2answers
94 views

How do I apply `FindFit` to data describing a spiral?

I have a list of numbers that, taken in order, describe a spiral in the complex plane. Here is a small subset of it, sufficient to illustrate the problem: ...
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0answers
50 views

How do I extract `Abs` and `Arg` values from this expression?

Let s = a + I*b be a complex number, with a and b both positive and real. I want to find <...
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1answer
73 views

Export ComplexPlot3D as Mesh with Material

If I generate a complexplot as follows: a1 = ComplexPlot3D[Log[z], {z, -5 - 5 I, 5 + 5 I}] I can export it to a 3D mesh (for use in external applications) with: <...
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1answer
75 views

Mathematica Kernel Aborting With ComplexPlot

I am trying to run the following line: ...
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1answer
148 views

How can I display conformal mapping? [duplicate]

z to quadratic function with conformal map. How to plot this in Wolfram Mathematica or Geogebra? Then I can write that code in $\LaTeX$. https://cmgreen.io/images/...
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2answers
308 views

Is it possible to define conjugate of a function?

Could you help me, please? I have two complex functions of real variable f[x] and fc[x] such that one is a conjugate of another one. I'd like to take a conjugate of an expression that includes both of ...
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0answers
39 views

Computing plane waves with the magnitude constant to 1

I have a question. In regards with the given computation, ...
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0answers
32 views

Plotting imaginary part on y-axis against real part on x-axis of complex momentum

I want to plot a complex momentum in complex plane where the y-axis shows imaginary values and x-axis shows the real values. I tried ReIm command but it plots Re and Im parts not Re vs Im. Below is an ...
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1answer
47 views

The value of the function with a very small Imaginary part but can be Plotted

I have a function Y[x_,β2_], It can be plotted normally. But when I take specific values, I get something like +0.000000*I when ...
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1answer
61 views

Extract real part of a complex function

I have a problem for extracting the real part of a complex number. The problem is the following: Suppose $f(z)=\frac{1}{z+\frac{\Delta_{1}}{z+\frac{\Delta_{2}}{z+\frac{\Delta_{3}}{z+...}}}}$, in which ...
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1answer
65 views

How to extract angle $0 \le \varphi < 2 \pi$ from a complex number $a + i \, b$?

Suppose you have a complex number of the standard shape $z = a + i \, b$ (where $a$ and $b$ are real numbers). How can we convert it to the polar shape $z = A \, e^{i \varphi}$? More specifically, I ...
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1answer
63 views

What results of FunctionMeromorphic are true?

Studying a new command of 12.2 FunctionMeromorphic, I try FunctionMeromorphic[(Re[z] - I*Im[z])/Abs[z]^2, z] ...
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1answer
86 views

Accurate Numerical values of a given functional

Consider the following functional : $$ I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy, s) − F(x −\mathrm iy, s)}{\mathrm e^{2πy}-1}, $$ where $ F(z, s) = \dfrac{\sin^2[π\Gamma(z)/(2z)]}{z^s} $....
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1answer
102 views

Derivative of -I (Log[-x] - Log[x]) - why is it zero? [closed]

Mathematica gives the derivative of the function -I (Log[-x] - Log[x]) as $0$, but on the real domain the expected result is $\pi\delta(x)$ and on complex domain it ...
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2answers
72 views

Drawing a straight line in complex plane

I have these point ...
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1answer
39 views

How can I understand the 2nd solution of this equation? (theoretically correct, but doesn't work while being verified)

I'm trying to solve these two equations: $$ \cos\left(\frac{\gamma'}{2}\right) = g_0\qquad e^{i\beta'}\sin\left(\frac{\gamma'}{2}\right) = g_1 $$ Where $g_0$ is real and $g_1$ is complex. From the ...
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0answers
31 views

Numerical errors in compiled function involving real and complex numbers as output

I am trying to use the Compile command in Mathematica to reduce the computation time because of its fast execution within Mathematica and ability to use the ...
3
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2answers
88 views

Comparison of Coefficients involving complex exponentials

I'm trying to solve a couple (independently) of equations of the following type $ a_0 x + 3 a_1 y(1 + xe^{i3q} + e^{-iq + 2ip}) + ... = 0, \forall x, y, q, p$. Using SolveAlways doesn't work well. So ...
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0answers
50 views

Maximize a function over complexes

Assume that I have a bounded real valued function $h(a,b)$ such that $a\in \mathbb{C}$ and $b\in [0,1]$. Can Mathematica maximize such function over $\mathbb{C}\times [0,1]$? I tried some functions ...
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0answers
64 views

One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
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1answer
24 views
0
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1answer
79 views

Principal value of a double integral numerically

I have several integrals of the form : where and . where a,b,wc and T are constants and PV denotes the Cauchy principal value I tried to integrate one of this form using NIntegrate however when ...
3
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2answers
81 views

plotting the Cayley Transformation

I'm new to mathematica and I have to plot the Cayley Transformation, which maps the upper half plane to the unit disk. I want to plot the z-plane and the w-plane. I wrote this: ...
5
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1answer
168 views

Visualizing convergence/divergence series

I was trying to visualize the idea of convergence/divergence of series using complex plane. I got this idea from “A First Course in Complex Analysis with Applications by Dennis Zill, Patrick Shanahan”....
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1answer
51 views

Integral of complex function

How to compute a complicated complex integral? You can see the example in the figure. I set assumptions that all constants are positive and real, then I try to integrate the $pel(z)$ expression but ...
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1answer
56 views

Real part of complex exponential

How do you obtain the real part of a complex exponential? For example, Mathematica gives $Re[e^{ik}]$ instead of $\cos(k)$, see figure. ...
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0answers
17 views

How to force N[ ] to output the real value (or all values) for negative cube roots [duplicate]

Evaluating N[(-1)^(1/3)] returns 0.5 + 0.866i in my v12.0 notebook. Of course, the equation x^3 = -1 has three distinct solutions for x. Is there a global (or local) option that will force Mathematica ...
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0answers
79 views

How to use _Complex types in CUDAFunctionLoad?

The documentation for CUDAFunctionLoad specifies various base datatypes you can use for your function's arguments, including ...

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