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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66 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
85 views

Export Long Plot with No Whitespace

Observe the following code: ...
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0answers
32 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
99 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
72 views
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60 views

how can I get an expression in the form of another expression

I need help solving this equation, I have done it by hand, but it is not very efficient to do. Express |z-i|=2|z+1| in the form |z+a|=b, where z ∈ C and a ∈ C and b ∈ R+ I used this: ...
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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
90 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
61 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
73 views

Mathematica Kernel Aborting With ComplexPlot

I am trying to run the following line: ...
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1answer
142 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
304 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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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
30 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
46 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
58 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
64 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
83 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
98 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
68 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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30 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 ...
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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
49 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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61 views

One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
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24 views
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1answer
61 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 ...
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2answers
80 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: ...
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1answer
159 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
49 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
52 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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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
76 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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114 views

Does anyone have a Mathematica implementation of the standard $\arg\zeta(s)$ function required to evaluate $S(T)$?

This question is related to my question Is there an elegant exact formula for the zeta zero counting function? on Math StackExchange. Question: Does anyone have a Mathematica implementation of the ...
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2answers
167 views

How do I analytically-continue the dilogarithm function?

Here's the dilogarithm definition: $$\text{Li}_2(z)=\sum_{k=1}^{\infty} \frac{z^k}{k^2};\quad |z|<1$$ However, the function can be analytically-continued by several integral means for all $z$ with ...
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1answer
84 views

Complex exponential plot

I don't know how to plot the exponential of an imaginary number. The function I've to plot is: Exp[-I w t]. I can give w a number, so I've chose w=1 and: ...
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2answers
493 views

Simplify 1+Sqrt[2]I-Complex[1,Sqrt[2]]

The expression 1+Sqrt[2]I-Complex[1,Sqrt[2]] should be zero. In fact, N[1+Sqrt[2]I-Complex[1,Sqrt[2]]] yields ...
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1answer
51 views

How to get rid of defects in that ComplexPlot3D?

I mean the result of ComplexPlot3D[Sin[z]/MittagLefflerE[10,z],{z,-1-I, 8 + I},Exclusions->None, PlotPoints -> 50] Its blow-up ...
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1answer
101 views

Formatting Imported Complex Arrays from Python (csv. files)

Just a short question, I am trying to import a complex array (matrix) from Python to Mathematica by first writing to a csv. file. When I Import the csv. array to Mathematica it is in a form (matrix ...
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3answers
612 views

How can I get the center and radius of this circle?

I am able to make Mathematica plot the solution to a complex inequality as the interior or exterior of a circle : Let $a$ be a positive real constant, and $f(z) = \frac{z+1}{z-1}$. I want to get the ...
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1answer
62 views

ComplexListPlot not complete

This code creates three complex lists. The third list is the Union of the other two. There are three plots. When applying ...
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0answers
49 views

Problem in FullSimplify with assumptions:

For the vector $\psi = \{ 0,F1,\alpha ,0,\beta ,0,0,F2\} $, I am trying to simplify ${\left\| \psi \right\|^2}$ where $\alpha = \cos (\theta )$, $\beta = \sin \left[ \theta \right]$, $F1 = {{\cos ...
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0answers
59 views

About what does FunctionSurjective think so long time?

Having tried a new in 12.2 command FunctionSerjective, I executed FunctionSurjective[z^(5/2), z, Complexes] // AbsoluteTiming ...
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0answers
89 views

Plot[Im[f[x]],…] incorrectly gives graph of identical zero function

Consider Plot[Im[(1 + (-1)^(2/3)*x)/((-1)^(2/3) + x)], {x, 0, 1}] At least in Mma 11 it gives the following picture: Meanwhile, ...
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1answer
40 views

Why is NSolve finding different # of roots for algebraic function?

Consider roots of $f(u)=u^{-1/4}-2/15 u-1/6$ which can be written as $$ u^{-1/4}e^{-1/4 (2n \pi i)}-2/15 u-1/6=0 $$ where $u^{-1/4}$ is taken as principal-value. Or as a GroebenerBasis: $$ f(u)=-...
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1answer
196 views

Program for efficient computation of given functional:

I need to plot the following functional with accuracy: $$ I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy,s) − F(x −\mathrm iy,s)}{\mathrm e^{2πy}-1}, $$ Where $ F(z,s) = \dfrac{1}{z^s\Gamma(\...
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2answers
151 views

Conjugation with real elements

Suppose I have an expression, such as A = 5 t^2 + 3 t + 4; I want to define the variable t to be real, therefore I can write ...
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1answer
260 views

Ugly streaks caused by Arg in a contour plot

I had a more general question about a similar problem more than two years ago, Getting rid of discontinuities in plots caused by square roots, logarithms, `Arg`, etc, which got lots of interesting ...

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