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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38 views

Force Mathematica to use only real valued intermediate values

I am trying to port a Mathematica expression to Python and eventually C++ code. I noticed that the expression can have some complex intermediate values, despite the final result always being a real ...
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0answers
75 views

Why is my plot hatched and how do I remove the hatched part of the plot? [closed]

Sorry for asking simple questions, I tried to solve it myself but I couldn't. I want to plot the following code, but the plot is hatched. ...
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1answer
57 views

How to recognize real parts of a function by plot?

I have this function f[x_] := ((2 x Cos[4 x] )/(1 + (x^2) ) + Sqrt[ Cot[3 x]^4 - (Cos[4 x]^2) (Csc[3 x]^2) ])/(4 /(x^2) + Cot[3 x]^2); where $0<x&...
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1answer
33 views

select the imaginary part of an exponential term

I have a list with exponential terms. This terms depend of real and imaginary parameters, for example: $ e^{\gamma_1 +\gamma_2 +iw_1+iw_2}$, $ e^{\gamma_3 +\gamma_4 +iw_5+iw_6}$, Is there a way to ...
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3answers
103 views

Incorrect limit in complex quantity

I have the following quantity $$ f = \frac{\exp(\sqrt{-k^2-i\epsilon}d)}{\sqrt{-k^2-i\epsilon}} $$ and form the limit as $\epsilon\to0$. Mathematica does not produce the correct result. Code: <...
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1answer
36 views

Plotting complex roots and domain

I'm trying to plot the roots of a complex equation, $p(z)=0$, and a domain, $D$, but have not found a clever way to cover general domains. If we, e.g., take the equation $p(z)=5 z^3 + 9 z^2 - 25 z + ...
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1answer
88 views

Evaluation of contour integral seems be incorrect

I am performing an contour integral of the form ...
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0answers
24 views
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1answer
61 views

How to plot residue of a complex polynomial which coefficients are function? [closed]

It is easy to find residue when we know roots of polynomials, such as : g[z_, t_] := 1 + t*z Residue[1/(1 + t*z), {z, -1/t}] <...
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0answers
41 views

Numerical estimates on a given functional [duplicate]

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{\sinh(\sin^2[π\Gamma(z)/(2z)])...
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1answer
56 views

Plotting the roots of polynomials which coefficients are functions [closed]

I am working on Mathematica just for few days and I am confused to plot the roots of a polynomial which coefficients are functions. In Mathematica examples, I found some simple examples such as : <...
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0answers
53 views

Indefinite integration giving expression in ArcTanh

I am using Mathematica version 12 and facing a problem which was not present in the previous version. I am performing indefinite integration $(x/((1-x^2)\sqrt{1+a^2 x^2+b^2 x^4}))$ and getting the ...
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0answers
26 views

Solving ODEs in the Complex Plane for General z

I saw with the new 12.0 update, they have introduced expanded functionality for solving complex ODEs. In the given example, they solve for $y(t)$ and plot results using the new ...
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1answer
60 views

How to fix this complex color function?

Currently, I am working of creating some tricky complex color function. I need the original values, not scaled, so I indicated ColorFunctionScaling->False, but ...
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0answers
32 views

Construction/good guess of a certain weight for a functional to satisfy given condition using numerics: [migrated]

Consider the following function : $$F(z) = \omega(z)\sin^2\left(\frac{π\Gamma(z)}{2z}\right)$$ Here, $\omega(z)$ is a weight we have to construct The following two condition should meet for $\...
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1answer
82 views

How to get rid of Conjugate in the result of Simplify? [closed]

FullSimplify[B^4 + A^3 E^(-I α) Conjugate[ AE^(-I α)], α ∈ Reals && A ∈ Reals && B ∈ Reals] I recently have the problem of simplifying a complex-...
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1answer
51 views

Hypergeometric function not giving a numerical value [closed]

I tried to run the following code: ...
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1answer
46 views

Using AbsArgPlot on parametricNDSolve output [closed]

I have solved following equation using ParametricNDSolve $$ \frac{\mathrm d^2y}{\mathrm dx^2} + \left(a + \frac{2}{\pi} b\ \arctan x\right)y = 0 $$ ...
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0answers
115 views

Numerical estimates on asymptotic of given functional as $x\rightarrow \infty$

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
116 views

Plot of a function defined by an integral

(First of all, this is my first Mathematica question. I'm not used to Mathematica that much. So, apologies in advance.) I need to plot the following functional with accuracy: $$ I(x,s) =\int_0^\...
2
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2answers
79 views

How to simplify this sums of exponentials?

I got expressions that look like $$ \frac{1}{2} \mathrm e^{-\mathrm i r x} \left[\mathrm e^{2\mathrm i r x} \left(1 + \mathrm e^{-2\mathrm i x}\right)^r + \left(1 + \mathrm e^{2\mathrm i x}\right)^r\...
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0answers
28 views

Errors in NDSolve for complex matrices

This is the problem. It is quite simple, and looks unwieldy only because I had to rewrite quaternions as complex matrices. ...
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0answers
33 views

Plotting a complex function under transformation

I am trying to plot the unit circle $\vert z\vert=1$ under the transformation $z\to z+\frac1z$ using mathematica. In general I want to plot a complex function $f(z)$ under the transformation $\phi(z)$....
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1answer
58 views

Mathematica image won't display

I need some help getting RegionPlot to display. Running this code: ...
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0answers
46 views

I want to plot root of the following complex equation

I am trying to plot the roots of the following equation as mentioned in the code below But it is not giving me output. If anyone can resolve this problem for me is most welcome. ...
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1answer
99 views

How to plot root of the complex equations

I want to plot the roots of the complex equation of a1. I have tried the following code but this is not giving me any result. I need bistable plot. How it is possible.? ...
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1answer
85 views

Cryptic NDSolve::nlnum when working with matrices

This problem was initially formulated in quaternions, but I had to rewrite them to complex matrices (as they seem to be supported better). Possibly introducing some errors along the way. So the ...
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1answer
42 views

How can I plot function density plot Hyper-geometric /Bessel function with complex arguments?

I am interested in the plot of a function in terms of hypergeometric and Bessel function with complex arguments, Here, it is my code, but the result is incorrect, the solution must be defined every ...
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1answer
50 views

How to chop complex number from solution solve using a model

Hi I have a set of 4 solution that was solved using a 4th order polynomial equation. I have noticed that some of the real number solution occurred through the list of 4 set of solutions. I have ...
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1answer
52 views

How do I expand expressions involving complex numbers?

I am trying to do the following: Expand[(A g + n)^2 Conjugate[A g + n]^2, Element[{A, g, n}, Complexes]] The goal is to expand and get all the terms of $(A g + n)...
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0answers
30 views

Inconsistency in complex line integral using 2 parameters vs 1 parameter

I am trying to numerically verify that, over a closed circular path, the line integral of a physics-inspired complex quantity $z_Q = P \cdot \frac{\partial}{\partial Q} S$ is the same regardless of ...
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2answers
100 views

Simplifying polynomial fractions with same `DiracDelta` function in both denominator and numerator

I am trying to simplify an expression with multiple Diracdelta functions in both numerator and denominator. For example, ...
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3answers
51 views
4
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1answer
65 views

Keep mesh of triangulation under complex valued transformation

I try to make a quick tool for "plotting" complex valued functions. Therefore I generate a Table of complex valued points lying in the complex plane building a ...
3
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1answer
102 views

Taking Real, Im, and Abs of polynomial fractions

I want to find out real imaginary and Abs of polynomial fractions composed of real-valued variables. For example, consider we have a polynomial fraction $f=\dfrac{a_1 +b_1 i }{a_2 +b_2 i }$ where $...
14
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2answers
314 views

Plotting Joukowski Airfoil Streamlines using conformal maps

I want to plot the streamlines around Joukowski Airfoil using conformal mapping of a circle solution. I do know that there are a lot of solutions to plot the airfoil itself (for example this), but I'...
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2answers
78 views

Obtain only positive complex solutions

By setting the determinant of a matrix to 0, I obtain 6 complex solutions for w and plot them. However, You can clearly see that the negative solutions mirror the positive solutions as the solution ...
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1answer
64 views

How to get Arg[I x] = Pi/2 for Real x? [closed]

The argument of 0 + I x should be Pi/2 for any Real x. How do we get Mathematica to evaluate it as such? ...
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0answers
55 views

How to find the derivatives from Solve after obtaining 6 complex solutions? [closed]

I have a 3x3 matrix. By setting the determinant to 0, I find the values of w in terms of ka and graphed the complex solutions. m, M, k, l are constants: ...
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2answers
52 views

How to separate the real part of elements in a list? [closed]

I have this list of complex numbers, and I like to just have the real parts. but this happens; ...
5
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0answers
104 views

Visualizing the Riemann's mapping theorem [closed]

The Riemann's mapping theorem allows to map any simply-connected domain in the complex plane $\mathbb{C}$ conformal onto the open unit disk. Conformal is meaning preserving angles. This is a complete ...
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1answer
44 views

How to use list of rules from solve to plot complex solutions?

I'm trying to find the frequency for three circular particles connected in a circle with different spring constants and different masses. After deriving the equations of motion, I get three complex ...
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2answers
91 views

How to plot a sequence of complex numbers?

I want to plot the complex sequence of numbers $(1/(1 + I))^n$ so that I can roughly see divergence/convergence. I tried DiscretePlot but doesn't seem to work.
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0answers
47 views

Getting rid of redundant complex values with FullSimplify

Main Problem I have a function $f(x,y)$ such that $f:\mathbb{R}\to\mathbb{R}$. However its expression contains redundant imaginary values and I have not been able to simplify it with Mathematica. The ...
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1answer
45 views

Converting coordinates in $\mathbb{R}^2$ to a point in $\mathbb{C}$ (and back again) [closed]

I have a list of control points for a BezierFunction. I want to apply a function taking input a complex number to these points and then plot the BezierFunction of the resulting points. I'm looking for ...
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1answer
23 views

Handling real parts in complex numbers [duplicate]

I have a problem understanding how Mathematica handles real values in complex numbers. E.g. ...
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1answer
77 views

Solving a well known transcendental equation [closed]

Evaluating Solve[E^(n t) == Cos[t] + n Sin[t], n] does not produce a solution for $n$. What method should be used to solve for the value of $n$?
1
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1answer
66 views

Indefinite Integration of real-variable function gives complex logarithm [closed]

Integrating real-variable function in Mathematica Integrate[1/Sqrt[2 x - x^2], x] gives following output with complex logarithm $$ \frac{2 \sqrt{x-2} \sqrt{x} \...
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3answers
89 views

Find residue at an essential singularity

I want to find Residue[(x^3 Exp[1/x])/(1 - x^2), {x, 0}] And when I try to evaluate this I have again: ...
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2answers
83 views

Abs[]^2 , Conjugate[], ComplexExpand[], and Simplify

I think this is a numeric problem but would like to see where it occurs. I create a complex rational polynomial as follows and make it a function of f ...

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