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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36 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
65 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 ...
1
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1answer
60 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
51 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
46 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; ...
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0answers
42 views

solve equation (or simplify) in real field still gives complex solutions (Solved) [closed]

Original post: I try to solve for this equations for $\sin\theta_1$ and $\cos\theta_1$, which should be a straightforward thing because it's nothing but a linear system ...
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0answers
54 views

Stieltjes inversion formula [closed]

I need to compute the Stieltjes inverse transform $$ -\frac{1}{\pi}\lim_{\beta\to 0^+}\int_{-\infty}^{\lambda} \Im (R(\alpha+i\beta)) d\alpha$$ for a resolvant $R$ of the form $$ R(z)=\frac{P_1(z)+...
5
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0answers
89 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 ...
0
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1answer
43 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
82 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
46 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
40 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 $n$?
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1answer
60 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} \...
1
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3answers
78 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
80 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 ...
1
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0answers
48 views

Defining dilogarithm with branch cut on $(-\infty,1)$

If my logarithms have a branch cut on $(0,\infty)$ then the dilogs constructed from these have a branch cut on $(-\infty,1)$. Is there a safe way to implement this in Mathematica? I tried with ...
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1answer
52 views

Animating roots of complex numbers

I have a list with complex numbers and I want to animate them. How can i do this? I would like to have appearing lines between points. I hope you know what I mean. Here is my code: ...
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0answers
45 views

Roots of complex numbers

My exercise is to find $n$ roots of a rank $n$ of a complex number. Here is my code: ...
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4answers
262 views

How to convert this term to a Hypergeometric function?

term=8*(-1)^(1/4)*Sqrt[b]*q0^(3/2)*\[Kappa]* EllipticF[I*ArcSinh[((-1)^(1/4)*Sqrt[b]*r)/Sqrt[q0]], -1] This is a physical term and it is not convenient to appear ...
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0answers
29 views

HermitianMatrixQ Ignores Assuming, $Assumptions

HermitianMatrixQ seems to ignore a variety of ways I tried to help it get the right answer. For example, ...
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1answer
55 views

Bug in FindRoot?

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2
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1answer
44 views

Solving complex trig quations - missing solutions?

{ Sin[Pi/2 + I*Log[2 + Sqrt[3]]], Sin[Pi/2 - I*Log[2 + Sqrt[3]]], Sin[Pi/2 + I*Log[2 - Sqrt[3]]], Sin[Pi/2 - I*Log[2 - Sqrt[3]]] } // FullSimplify ...
4
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2answers
180 views

Better way to treat branch cut problem in Mathematica

Currently, Mathematica treats function which has branch cuts; $\log(z)$,$\sqrt[n]{z}$, etc, by taking its principal value. This may cause a problem in Contour integration when the path of integration ...
0
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1answer
62 views

How to substitute by NDSolve solution to plot a new function

Assume I got some function by NDSolve , like y(t) ...
4
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1answer
95 views

Real and imaginary parts of complex logarithm

I need to obtain the real and imaginary parts of the below expression with Mathematica: $(- i a - m^2) \ln(\frac{i m^2}{2 a})$, where $a$ and $m$ are real. So we have: ...
2
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2answers
47 views

Convert string of tuple of numbers to complex number

I am reading complex number from a file which gives me a list like that ...
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2answers
62 views

No result returned on ContourPlot with specific relation [closed]

For reference, I am using Wolfram Mathematica 12.0. I am attempting to plot the complex subset defined by: $|z+6|+|z-6| =1$ where z is a complex number $z = x+ i y$. Utilising ContourPlot directly ...
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1answer
73 views

How to chop a complex number?

I'm solving some differential equations by iterating and I want to use Chop to get rid of noice smaller than a certain threshold. However, I found that Chop only "chops" the real part, not the ...
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3answers
879 views

Modify real part and leaves imaginary part unchanged

How can I flip the sign of the real part but not affect the imaginary part of a complex number: a+bi => -a + bi Example list: ...
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1answer
81 views

Contour plot of streamfunction

I am trying to obtain a graph similar to this one: ...
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0answers
41 views

Manipulate and Parametric plot not show anything.Why?

My aim was to map a semi ellipse to a semi-circle, for different values of ellipse parameters to a circle of different radius. So I have written a code in Mathematica. ...
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0answers
38 views

Plotting NDSolve function in complex coordinates

I have this system of equations: $- \ddot{z} + \frac{1}{g} \frac{\partial g}{\partial z} \dot{z}^2 + \frac{1}{g} \frac{\partial g}{\partial z^*} \dot{z} \dot{z}^*$ =0 , $- \ddot{z}^*+ \frac{1}{g^*} ...
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2answers
111 views

Linear fit statistics for a complex data set

I am having some technical and conceptual troubles in using NonlinearModelFit with a complex data set. I have a 2 dimensional array where the two positions are complex numbers, such that: ...
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3answers
78 views

Riemann surface of incomplete gamma function

Michael Trott in his book The Mathematica GuideBook for Symbolics, page 1003, has illustrated a nice way to visualize the Riemann surface of the incomplete gamma function $\Gamma[\alpha, z]$. To plot ...
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1answer
82 views

Plotting a function in 3 dimensions within a domain

In this paper: https://www.staff.science.uu.nl/~beuke106/HypergeometricFunctions/COGP.pdf Any help how to reproduce the plot in Figure:7 It’s the leading order of the complex function, Equation (...
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1answer
116 views

Can I numerically solve these equation in Mathematica? [closed]

I have this couple of equations : $ \partial_\mu \partial^\mu z^i + G^{i\bar{p}} (\partial_j G_{k\bar{p}} ) \partial_\mu z^j \partial^\mu z^k + G^{i\bar{j}} (\partial_{\bar{j}} G_{k\bar{l}} ) \...
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0answers
45 views

Solving differential forms equations

I have this couple of equations in differential forms language: $ \Delta z^i \star {\bf{1}}+ G^{i\bar{p}} (\partial_j G_{k\bar{p}} ) dz^j \wedge \star dz^k + G^{i\bar{j}} (\partial_{\bar{j}} G_{k\bar{...
3
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1answer
127 views

how To Improve that ComplexPlot3D

I have in mind the result of ComplexPlot3D[Log[MittagLefflerE[1/2, z]],{z, -50 - 50*I, 50 + 50*I}, PlotPoints -> 300,PlotRange -> All] In particular, the ...
1
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1answer
37 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 ...
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1answer
32 views

Get Conditions for Variable to be Real

I have a complex definition of a few variables (that I got using s = Solve[1 - a x^2 - x^3 == 0, x]) and I now want to know under what conditions of "a" will each ...
0
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1answer
53 views

Remove +0Is from Root function

I'm trying to find the zeros of the eigenvalues (functions of $k_x$) of a self-adjoint $4\times4$ matrix H: ...
4
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1answer
105 views

Mathematica not simplifying rational powers in complex expressions

I have the following expressions and I would like to obtain a final result purely in the real domain. ...
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0answers
32 views

How to compute Bott-Chern operator ddc

I wish I could make Mathematica compute the $dd^c=2i\partial\bar\partial$ of a function depending on several complex variables. The question involves complex or Wirtinger derivatives (https://...
3
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1answer
98 views

Problem with complex eigenvalues in periodic Sturm-Liouville problem

I'm having trouble using NDEigenvalues to obtain the first few eigenvalues for a differential operator on the circle of radius one-half. $\qquad Lf(x) = f''(x)+ (-...
1
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1answer
60 views

visualizing branch cut of a complex function

I'm working in the plotting the branch cut of a complex function, namely: $w(z) = (2+z) \ln(2+z) - 2(1+z) \ln(1+z) + z \ln z$. To do so, I have tried this: ...
9
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1answer
293 views

Why ArcTan[1, 0. I ] yields -1.5708+0. I?

Bug introduced in 5.2 or earlier and persisting through 12.0.0 Why ArcTan[1, 0. I ] yields -1.5708+0. I ? The result should ...
0
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3answers
81 views

expression containing radicals of imaginary numbers

I can't bear an expression containing radicals of imaginary numbers, in case it can be expressed as in terms of radicals of real numbers only. For example, I can't bear the expression ...
5
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1answer
137 views

Visualizing Riemann surface (two branches) of logarithm

I'm trying to plot two branches of the complex multi-valued function: (In a previous post - linked above-, Mathematica found the branch cut of the following function between -1 and 0) $1-z\ln[(1+z)/z]...