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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1answer
31 views

ContourPlot of a polar flow field (complex function)

I am currently trying to contourplot a dimensionless velocity-field given as: ...
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2answers
114 views

Plotting transformations of loci in a complex plane [closed]

I found the solution to plot loci of complex numbers here, e.g. a locus of points of $z$ given $|z|=1$ is a circle centered at the origin with a radius 1. But I am struggling to plot transformations, ...
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58 views

Numerical integration with poles

I have got many errors for this integral. Anyone knows how to fix it? (I am using mathematica12.2) ...
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43 views

Defining branch cut continuously

I'm considering a complex number of the form $z = e^{2Ix}$. I can plot the circle(or partial-circle) this draws out as you increase x by doing a parametric plot of the real and imaginary components of ...
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38 views

Convert complex exponential to real exponentials, sines and cosines

While taking the inverse Laplace transform of certain expressions, Mathematica yields complex exponentials. For example, using the following code: ...
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1answer
79 views

How can I derive all the roots of a complex equation containing the square root of Sinh^2 using Mathematica [closed]

I have the following equation: where m,n are arbitrary natural numbers and beta and k are positive nonzero real numbers. How can I find all the roots of this equation using Mathematica?
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1answer
49 views

NIntegrate giving different results after a change of variables

When I compute numerically the following double integral: \begin{equation} f(x,y)=\int_{-\infty}^{+\infty}da\int_{-\infty}^{+\infty}db\, \cosh\left[\frac{\sinh^{-1}(a)-\sinh^{-1}(b)}{2}\right]\, \exp\...
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1answer
36 views

How can I use ComplexExpand and PowerExpand for Log of complex symbols?

How can I simplify Log[ x + I y] or Log[ r Exp[ I phi] into Log[r] + I Log[ phi] where r = Abs[x + I y] and Phi = Arg[x + I y] using ComplexExpand, PowerExpand, etc... };
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2answers
77 views

Speeding up ComplexExpand

I have a code where I have to take the dot product of two lists, that contain some symbols, and then use ComplexExpand. For a long list it take a very long time and ...
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2answers
99 views

Solve Equations using Mathematica

Good day. I have a question of how to get the algebraic expressions for $a$, real part $b$ (denoted $Re(b)$), and imaginary part $b$ (denoted $Im(b)$). Let's say $a$ is a real number and $b$ is a ...
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1answer
57 views

The function Norm is giving complex numbers as output [closed]

I'm trying to find the norm of a complex vector ...
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1answer
51 views

Getting strange result with derivative of Abs of a complex number

So I am getting some results after a computation like: (-0.741446 - 5.47358 I) Abs'[-0.702207 + 0.0951203 I] The problem is the derivative in ...
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38 views

Using Mathematica to compute limit of complex number that involves symbols

I want to use Mathematica to compute the Marchenko-Pastur density from its Stieltjes transform. The process is described in https://terrytao.wordpress.com/2010/02/02/254a-notes-4-the-semi-circular-law/...
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56 views

Calculating complex integral representation of the Hankel function of the first kind

I was wondering if any one can help me calculate this integral using Mathematica. This is a form of integral representation of Hankel function of first kind: ...
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1answer
68 views

How to solve complex least squares with real unknowns

I am looking at the case where my least squares problem is of the form $ y=A x $ where y is a vector of measured complex values, A is the model or design matrix, also complex, and x are the model ...
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2answers
67 views

Error complex function ERFI(X): looking for alternative function representations?

I have some analytical results from a physics problem, where the Mathematica gives the results in terms of complex error function. I would like to explore another function representation using ...
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3answers
147 views

Plotting the solutions of the equation $e^{-z}=z$ in the complex plane

I would like to plot in the complex plane the solutions of the equation $$e^{-z}=z.$$ I tried this: I took $z=a+ib$ and took the real and imaginary part of the equation: ...
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1answer
90 views

Cos[sqrt[-x]] == Cosh[sqrt[x]] but not Cos[sqrt[-(x+y)]] == Cosh[sqrt[(x+y)]]?

I have trouble with the following apparent contradiction: ...
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4answers
196 views

Differential Equation in Complex Plane

I asked this question 8 years ago, but the answer of @Jens was not satisfactory and it didn't reproduce the plot exactly. I'm wondering if new versions of Mathematica can handle it.
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1answer
53 views

Problem with numerical ConjugateTranspose?

Suppose I have a normalized numerical array, B1, ...
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2answers
74 views

Compute real and imaginary part of parametrized complex rational expression

I would like to compute the real and imaginary part of a complex valued rational function $Z_b=\frac{1}{\frac{1}{\frac{1}{C_1 \text{i$\omega $}}+L \text{i$\omega $}+R}+C_2 \text{i$\omega $}}$ that ...
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2answers
57 views

complex region plot - tweaking

ComplexRegionPlot[Abs[z + 1 - I] <= 1, {z, -2, 1 + 2 I}, AxesOrigin -> {0, 0}, AspectRatio -> 2/3] ComplexRegionPlot[Arg[z - 1] <= 3 Pi/4, {z, -2, 1 + 2 I}, AxesOrigin -> {0, 0}, ...
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0answers
55 views

Choose branch cut of sqrt so that function is continuous?

I am willing to plot the following function ...
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1answer
127 views

Why Mathematica does strange thing with complex numbers [duplicate]

For example, compare the two commands below. ...
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2answers
63 views

How to solve system of equations with complex variables

I'm trying to obtain the solution to the following system of 3 equations and 4 variables: ...
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1answer
119 views

How can we obtain the imaginary part of a too complicated expression with Mathematica?

I would like to obtain the imaginary part of a long expression. All the parameters in the expression are real. Moreover, X and Y are positive. I have used ComplexExpand and tried to simplify the ...
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1answer
56 views

Working with complex functions and complex conjugation

I have a complex function and I want to take a list of derivatives of it. My code reads as follows: ...
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2answers
118 views

Find the $z$ such that $|z + a| \leq |z| + |a|\cos(\arg(z))$

Find the $z$ such that $|z + a| \leq |z| + |a|\cos(\arg(z))$. My approach is to use Resolve: ...
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1answer
49 views

Plot Arg[z] in three dimensions

I would like to plot the function Arg[z] for a complex number $z$ in three-dimensions: I would like to obtain it as a surface over the complex plane, as in the &...
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1answer
107 views

Equation solving with magnitude constraints incredibly slow

Somewhat complicated question and sorry in advance if it is presented poorly. I'm running Mathematica 12.0 (haven't updated to 12.1 yet). I'm trying to solve a set of linear complex equations with ...
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0answers
90 views

Solving set of equations with complex variables (looking for critical points)

I need to solve (a more complicated version of) the following set of equations : ...
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3answers
97 views

Importing complex numpy arrays

Related question: Formatting Imported Complex Arrays from Python (csv. files) I am trying to import a large numpy array to Mathematica but the strategy in the question above is far too slow. For a 100-...
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0answers
46 views

Conjugate transpose of noncommutative matrix multiplication

I have: $$p=iab$$ $p,a,b$ are operators. So in mathematica I am writing this as: p=I*a**b Conjugate of above is $$-iba$$ In mathematica I tried ...
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2answers
56 views

Issue visualizing the image of a vertical line under 1/z using ComplexContourPlot

I am using the function ComplexContourPlot to try to get the image of a vertical line under 1/z however I am getting an error. In this case I would like to see the image of 1/z for the vertical line ...
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1answer
46 views

ComplexListPlot not ploting [closed]

In a nutshell i have to plot a sequence of complex numbers to roughly see if it converges or not. I've created the list using the following ...
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0answers
95 views

Why is ComplexQ not available? [closed]

For names = Names["System`*"]; executing the following returns 200 hits. ...
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3answers
198 views

Removing complex numbers from a set

I have the following list: ...
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0answers
75 views

Plot image of complex function

I have a set $S$ and a complex function $f$. How can I use mathematica to visualise $f(S)$? Using ComplexPlot doesn't do what I want, the set in the picture doesn't change, only the colouring of it, ...
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1answer
49 views

Simplification of conjugate expression with integers

I have a long expression that contains $(-1)^q$, where $q$ is an integer. I'm taking conjugate of this expression, and Mathematica gives me the term Conjugate[(-1)^q]. And, of course, I'd like to get $...
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1answer
128 views

How to plot the Worm domain?

While reading Krantz' "Harmonic and Complex Analysis in several variables" I stumbled upon the Worm domain. It is a counterexample to the long-believed statement that a smoothly bounded ...
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2answers
154 views

Equality of two lists of complex numbers

I have these two lists of complex numbers: ...
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1answer
36 views

Coloring in ComplexListPlot

I want to plot the points of a complex sequence with colors changing from point to point. I tried ...
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1answer
61 views

Laurent Series with Assumptions

I want to obtain the Laurent of the function f(z) = 1/(z(z-1)) valid first in 0 < Abs[z] < 1 and second in ...
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2answers
51 views

Reading File of Complex Numbers

I have a text file "IQ256.txt" with the following format (one complex pair per line): -23636.100 13359.055I -25478.040 9342.004I -26637.370 5257.033I -27184.020 1087.021I -27069.778 -2976....
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1answer
95 views

Integrations done by residues and numericals don't agree

I want to integrate $$ \int_{-\infty}^{\infty} dw \hspace{0.51em}\frac{w^{n} e^{i wt}}{(w^{2}-\Omega^{2})^2 +(\gamma w)^2} $$ I did so using contour integration because it has the poles: $$w=\mp \frac{...
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3answers
221 views

Plotting an oriented contour

I'd like to add at least one arrow to a closed contour in the plane to show that e.g. a circumference is counterclockwise oriented. If I use e.g. ...
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1answer
99 views

Solve A System of Trigonometric Equations

I tried running the following code on Mathematica Cloud, but it didn't because it was taking long of I have the basic plan. Would someone please run this code for me and share with me the results. it'...
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2answers
87 views

Algebraic form of complex number

I want to obtain the result of a definite integral as a complex number expressed in the algebraic form. I tried: ...
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3answers
104 views

ComplexFit fits only part of fit parameters

I'm trying to fit experimental complex data with model: model = s/(1-I*t*fr) In the model I want to find real-valued parameters ...

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