# 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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### 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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### 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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### 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? ...
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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### 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; ...
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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### 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: ...
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 ...
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 ...
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: ...
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: ...
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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### 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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### 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 ...
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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### 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 ...
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### 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 ...
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 ...
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### 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: ...
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. ...
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://...