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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205 views

Why does Mathematica choose branches as it does in this situation?

Consider these integrals: ...
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1k views

How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
9
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546 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitely. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
3
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269 views

Taking real and imaginary parts of indexed functions and speeding up ComplexExpand

I am setting up a large system of ODEs and in order to use the IDA method (which is sig. faster for my system and thus attractive), I must split my equations into real and imaginary parts. I am ...
2
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94 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
2
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0answers
369 views

How to make the imaginary part of a +0. I zero globally?

Values like a +0. I are really annoying. Answers from How to reduce expressions with complex coefficients in the form of a+0.*I? Is there a way to globally set when to treat a very small number as ...
2
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0answers
371 views

Simple contour integral with a parameter gone wrong

I run into the following problem, I tried to evaluate a very simple integral: Assuming[ a > 0 , Integrate[Sin[a*s]/(s - I)^2, {s, -Infinity, Infinity}]] ...
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0answers
50 views

Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
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72 views

The number of real values assumed by combinations of complex roots of a decic

Define complex conjugate as the pair of complex numbers $a+bi,a-bi$. Assume you have 5 such pairs and they are the 10 roots $x_i$ of a 10th-deg equation with integer coefficients. In general, how many ...
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34 views

Simplification of a complex-valued expression with purely real components

(I'm including all the information here, as I'm not sure how much of it is necessary to solve the problem. For a tl;dr skip to the bottom) I've been working on a problem involving calculating ...
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0answers
62 views

ComplexExpand does not treat everything as real number

ComplexExpand does not treat everything as real number?? Please read the following simple example ...
0
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0answers
92 views

Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form $$\left\{ \begin{align} i\frac{da_1}{dt} ...
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65 views

Why does this integral have a complex result

I wanted to find the normalization of distribution F2 . ...
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82 views

Complex integrals and residues

I have a question. I try to integrate this function: Integrate[Exp[I k z]*Exp[-Sqrt[k^2 - A^2]x]*Exp[-k^2*L^2/4]/Sqrt[k^2 - A^2], {k, -Infinity, -A}] But ...
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121 views

A power series expansion

Consider the function, $f(z) = z tanh(\pi z) log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ and ...
0
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76 views

About how Mathematica understands the branchcuts of the complex logarithm [Part 3]

One understands that for the function $\log(z^2+a^2)$ Mathematica implicitly puts the branch cuts to be starting at $\pm ia$ and going up/down respectively on the imaginary axis. The phase of this ...
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747 views

Fastest way to create a NxNxNxN dimensional matrix

I have a function that outputs a complex number Func[x_,y_]:= blah blah; I have constructed a table of all possible values of this function. ...
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89 views

How does Mathematica understand branchcuts of the complex logarithm? [Part 2]

I observe that the answer generated by the first integration is not in any simple way related to the next two answers. (some simple jump of i 2\pi across the branchcut of the logarithm is not helping ...
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124 views

Alternate method of conjugation using replaceall

Mathematica really struggles to simplify complex conjugates of complicated expressions - even given assumptions for every symbol in the expression being real. Often times I've found that I can ...
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0answers
153 views

Assigning numerical values to constants results in complex coefficients in Equations of Motion

I am using Mathematica to get the Equations of Motion (EOM) for a mechanical system (using Lagrangian Mechanics). While I get the EOM in symbolic form, on introducing the following code for assigning ...
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110 views

Precision of a complex number

In an output I'm getting a number like -0.33998187034939803 + 0.I. Finding ...
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381 views

Solve equations real and imaginary part separately

For my system of equations, the procedure described in Solving complex equations of using Reduce works no more. How can I separate the real and imaginary part of ...