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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7
votes
1answer
188 views

Testing for primality in quadratic rings?

Testing for primality in $\mathbb{Z}[\sqrt{-1}]$ in Mathematica is easy: PrimeQ[n, GaussianIntegers -> True] But how can I test for primality in, say, ...
8
votes
1answer
295 views

Symbolic Integration along contour: branch cut problem?

Context Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as ...
8
votes
0answers
470 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 $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
4
votes
1answer
633 views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
2
votes
1answer
528 views

Finding residues of multi-dimensional complex functions

Say I have a function $f$ of $n$ complex variables, $\{ z_i \}_{i=1}^{i=Nc}$. And then I want to contour integrate the expression such that for each $z_i$ its an integration on an unit circle about ...
7
votes
1answer
674 views

Is Abs[z]^2 a bad way to calculate the square modulus of z?

For a numerical quantity z, Abs[z] returns the square root of the sum of the squares of the real and imaginary parts of ...
3
votes
2answers
400 views

Is there a way to solve the Apollonius Circle problem in Mathematica?

Assuming x, a, and b are complex numbers, is there a way to reduce the equation Abs[x - a] == k Abs[x - b] to something like ...
4
votes
3answers
2k views

How can I plot the complex graph of $x^x$ in Mathematica? [duplicate]

Possible Duplicate: How to plot imaginary part of a function Plotting Complex Quantity Functions For example, this Wolfram Alpha query shows this graph: But it does not show the code for ...
2
votes
0answers
341 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}]] ...
6
votes
1answer
1k views

Complex number operations: telling Mathematica variables are real

I want to do Conjugate[a + b*I], but when I do that, the solution is Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
0
votes
2answers
359 views

Mathematica Plotting of complex and convolution integrals

I was trying to plot the following: ...
43
votes
4answers
4k views

How can I generate this “domain coloring” plot?

I found this plot on Wikipedia: Domain coloring of $\sin(z)$ over $(-\pi,\pi)$ on $x$ and $y$ axes. Brightness indicates absolute magnitude, saturation represents imaginary and real magnitude. ...
6
votes
1answer
144 views

How to reduce expressions with complex coefficients in the form of a+0.*I

I'm trying to get an eigenvalue equation in Mathematica, and the result is an expression with coefficients of the form a + 0. I. For example, Is there any clever ...
11
votes
2answers
2k views

Plotting complex Sine

I've got another plotting problem. I want to plot Sin[z] where z is complex. So, I've tried the following: ...
0
votes
1answer
255 views

Get Mathematica to simplify $\cosh(i x)$ [closed]

I want Mathematica to simplify Cosh[I x] to Cos[x] if I tell Mathematica that x is Real. I ...
7
votes
1answer
928 views

Is it possible to set a variable as a positive one in the whole notebook?

I'm having issues during integration due to the fact that Mathematica doesn't know if an undefined variable is positive or not (it gives me complexes which bothers me in the end). For example I do ...
4
votes
4answers
2k views

Solving complex equations

I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce. ...
4
votes
1answer
488 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
5
votes
3answers
3k views

Is there a simple way to plot complex numbers satisfying a given criteria

I think this should be straightforward, but I cannot seem to find a good source on how to do it after searching around, so I'm trying to sketch sets of complex numbers that meet a given for criteria. ...
18
votes
3answers
1k views

Visualizing a Complex Vector Field near Poles

I've been playing around with a visualization technique for complex functions where one views the function $f: \mathbb{C} \rightarrow \mathbb{C}$ as the vector field $f: \mathbb{R^2} \rightarrow ...
31
votes
6answers
4k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
8
votes
3answers
2k views

Derivative of real functions including Re and Im

When deriving functions using Re, Im or Arg (and probably some other functions as well), ...
11
votes
4answers
6k views

Plotting Complex Quantity Functions

Trying to plot with complex quantities seems not to work properly in what I want to accomplish. I would like to know if there is a general rule/way of plotting when you have complex counterparts in ...
4
votes
2answers
234 views

presenting a real number as real instead of imaginary

I have an equation which results in an answer of the form $\frac{i a}{\sqrt{c-d}}$ is there any way to get Mathematica to present it in it's real form? like $\frac{a}{\sqrt{d-c}}$ I know that I ...
11
votes
2answers
3k views

How to specify assumptions before evaluation?

If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example : ...
8
votes
2answers
850 views

RootSearch for complex or multiple equations

First the background. I'm trying to solve for the roots of a rather messy complex equation. This is not the exact equation, but it's a decent (simpler) stand in: ...