# 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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### 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 ...
85 views

### Export Long Plot with No Whitespace

Observe the following code: ...
32 views

### Export 3D Mesh without shading issues

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

### Why is ComplexPlot So Slow?

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

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### 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: ...
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 ...
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: ...
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 <...
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: <...
73 views

### Mathematica Kernel Aborting With ComplexPlot

I am trying to run the following line: ...
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/...
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 ...
39 views

### Computing plane waves with the magnitude constant to 1

I have a question. In regards with the given computation, ...
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 ...
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 ...
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 ...
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 ...
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] ...
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 $F(z, s) = \dfrac{\sin^2[π\Gamma(z)/(2z)]}{z^s}$....
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 ...
68 views

### Drawing a straight line in complex plane

I have these point ...
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 ...
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 ...
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 ...
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 ...
61 views

### One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
24 views

### Prove that for complex numbers you can apply the formula for the difference of squares [closed]

a^2-b^2=(a-b)(a+b) a in R, b in C
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 ...
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: ...
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”....
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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
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: ...
493 views

### Simplify 1+SqrtI-Complex[1,Sqrt]

The expression 1+SqrtI-Complex[1,Sqrt] should be zero. In fact, N[1+SqrtI-Complex[1,Sqrt]] yields ...
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 ...
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 ...
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 ...
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 ...
49 views

For the vector $\psi = \{ 0,F1,\alpha ,0,\beta ,0,0,F2\}$, I am trying to simplify ${\left\| \psi \right\|^2}$ where $\alpha = \cos (\theta )$, $\beta = \sin \left[ \theta \right]$, $F1 = {{\cos ... 0answers 59 views ### About what does FunctionSurjective think so long time? Having tried a new in 12.2 command FunctionSerjective, I executed FunctionSurjective[z^(5/2), z, Complexes] // AbsoluteTiming ... 0answers 89 views ### Plot[Im[f[x]],…] incorrectly gives graph of identical zero function Consider Plot[Im[(1 + (-1)^(2/3)*x)/((-1)^(2/3) + x)], {x, 0, 1}] At least in Mma 11 it gives the following picture: Meanwhile, ... 1answer 40 views ### Why is NSolve finding different # of roots for algebraic function? Consider roots of$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: $$f(u)=-... 1answer 196 views ### Program for efficient computation of given functional: I need to plot the following functional with accuracy:$$ 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(\...
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 ...