Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.
26
votes
6answers
2k 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 ...
9
votes
4answers
3k 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 ...
3
votes
1answer
328 views
Symbolic integration in the complex plane
Context
While answering this question, I defined (symbolic and numerical) path integrations as follows
...
36
votes
4answers
2k 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.
...
17
votes
3answers
708 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 ...
8
votes
3answers
330 views
How can I convert a complex number a+b I to the exponent form A Exp(I phi)?
When I have an expression such as:
(1/4 + I/4) ((1 - 2 I) x + Sqrt[3] y)
it is hard to get an intuition of the number.
So I want to convert it to the complex ...
4
votes
4answers
1k views
Plotting an Argand Diagram
I have the function:
$F(\omega) = \frac{5\; - \;i\;\omega}{5^2\; +\; \omega^2}$
When $\omega$ has the values :
$\{ -7, -2,\; 0,\; 2,\; 7\}$
How would I plot the Argand diagram in Mathematica? Or ...
9
votes
2answers
1k 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 :
...
5
votes
1answer
484 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 ...
7
votes
3answers
998 views
Derivative of real functions including Re and Im
When deriving functions using Re, Im or Arg (and probably some other functions as well), ...
2
votes
1answer
253 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 ...
8
votes
1answer
374 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
1answer
364 views
Does the Im function work with symbolic arguments?
Does the Im function work with symbolic arguments?
...
3
votes
2answers
182 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 ...
2
votes
2answers
304 views
Eigensystem, Eigenvalue doesn't output nonreal eigenvalues
Basically I have a matrix and when I used either Eigenvalue or Eigensystem, it doesn't output nonreal eigenvalues, instead it ...
10
votes
2answers
714 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
420 views
Complex line integral
Can someone recommend an online article or introductory tutorial that will show me how to do real and complex line integrals using Mathematica?
7
votes
1answer
234 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
...
6
votes
1answer
112 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 ...
5
votes
2answers
166 views
How to eliminate the zero real part of a purely imaginary number?
In Mathematica 9, a purely imaginary number, e.g. 0.9 I, will display as 0. + 0.9i in the output form. How can I eliminate the ...
3
votes
1answer
105 views
Exporting/Importing a Table of complex numbers
I'm generating a long table of list of the form:
PN={{1,2,1+i},{3.5,2.6,2}...},{...},...
Using:
Export["PN.dat", PN, "Table"]
...
3
votes
4answers
867 views
Solving complex equations
I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce.
...
0
votes
2answers
50 views
Conjugate and simplify
I want to get a cosine from taking the real part of a complex exponential: $cos(x) = Re(exp(i x))$. What I do in Mathematica is
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