Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.
1
vote
1answer
49 views
Overloading conjugate operator for a particular function
I trying to modify the behaviour of the built-in Conjugate[] operator on a particular function I have defined, to take into account that some of its variables are real.
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1
vote
3answers
86 views
finding an argument of a complex number
What is the simplest way to find the argument of the following function?
((1 - E^((I π (1 - α))/(β - α)) z)/(1 - E^(-((I π (1 - α))/(β - α))) z))
as I tried the ...
2
votes
0answers
77 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 ...
1
vote
1answer
92 views
why there is a small imaginary part [closed]
I encountered a problem. I have a eigenvector eigvsI[1]
...
0
votes
0answers
76 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 ...
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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3
votes
3answers
125 views
How to extract phase angle from sinusoid
I'm doing some electric circuit calcualtions and I'm trying to get the phasor representation of some arbitrary function of Sin or Cos. Could be complex like:
...
1
vote
0answers
70 views
ComplexExpand absolute squared
ComplexExpand[Abs[a + b I]]
Gives
$\sqrt{a^2 + b^2 }$
ComplexExpand[Abs[a + b I]^2]
On the other hand gives
Abs[a ...
1
vote
2answers
74 views
How to take conjugate of a function?
Naïvely this is what happens and it obviously is not helpful!
...
1
vote
1answer
97 views
Plotting a complex function [duplicate]
What does it mean if this message appears:
{Im[(1-E^Times[<<3>>] f)/(1-Power[<<2>>] f)]-0,Im[(1-E^Times[<<3>>] f)/(1-Power[<<2>>] f)]-0} must be a list of equalities or ...
0
votes
1answer
130 views
ContourPlot with parameter
I have an equation for function F[x,y]==0 which first argument x is real and another, y, ...
0
votes
1answer
85 views
Simplifying Complex Numbers that contain physical units
I am trying to evaluate the following:
Simplify[Meter Nano Re[(a + I b)/(Meter Nano)], Assumptions -> Element[{a, b}, Reals]]
However, Mathematica returns:
...
4
votes
2answers
139 views
Convergence and value of a complex power series
I've done a little math and I got the following power series expansion of $\log z$ about $z_0=-2+i$.
$$\log z=\log(-2+i)+\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n(-2+i)^n}[z-(-2+i)]^n$$
I've shown that ...
2
votes
5answers
409 views
Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do? [closed]
The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration.
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0
votes
0answers
66 views
Choosing the appropriate solution for the square root [closed]
My problem is the following: given the function
myfunc[x_, a_]:= (a^3 - (a^2)^(3/2))/(x)
the limit as x goes to 0 should be well defined and = 0. However,
...
5
votes
1answer
255 views
How do I put an image on the complex plane?
I watched this video and became interested in transforming an image. But I have no good idea on how to embed an image in the complex plane using Mathematica.
I have a method that seems to work, but ...
15
votes
2answers
211 views
Inconsistent results from equivalent integrals
Why is Mathematica returning different values for these two integrals:
I am just being introduced to complex integration, so it's possible that I have a misunderstanding of how this works, but in ...
8
votes
2answers
157 views
What is the value Re[Sqrt[1+I*2*x]]?
When I try to evaluate Re[Sqrt[z]], for some values of Mathematica fails to evaluate it.
For example,
Re[Sqrt[2 + I*x]]`
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4
votes
6answers
339 views
Image of first quadrant under $f(z)=(z+i)/(z-i)$
I'm able to plot the region where Im[z] > 0 and Re[z] > 0:
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7
votes
3answers
117 views
Wrapper for inexact numeric complex numbers that maintains polar form
Related question:
How can I convert a complex number a+b I to the exponent form A Exp(I phi)?
Mathematica insists on displaying complex number in form a+I b when ...
4
votes
2answers
159 views
What can I do to eliminate the error FindFit::nrjnum:?
I am testing the "Power Law with finite-time singularity" hypothesis for world population growth for a project.
The data I'm using (same behaviour should also be exhibited by the stock market, thats ...
1
vote
1answer
130 views
Stop Mathematica from giving imaginary solutions
I have the following equation:
$$D=\frac{1}{64} \pi A ^3 B \sin \left(C\right)-\frac{1}{2} \pi A B \sin \left(C\right)$$
which I want to solve for $A$. The equation is cubic in $A$ so this should ...
1
vote
1answer
123 views
How can I get the solution of complicated implicit function?
The question is what is the method to solve the implicit function has real and imaginary number.
For example, The function is F(x,y)=(-I*x + 2*y^2)^2 + x^2 - 4*y^4*Sqrt[1 - I*x/(y^2)].
Although I ...
6
votes
1answer
116 views
Compiling Error functions of complex values
According to List of compilable functions Erf and Erfc are compilable functions.
However, I want to make a compiled version of ...
0
votes
1answer
418 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?
5
votes
2answers
285 views
0
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0answers
41 views
Contour integration [duplicate]
Possible Duplicate:
Symbolic integration in the complex plane
Does mathematica do Contour integration ? like this one :
$\displaystyle \oint_{\gamma} f(z)\ \mathrm{d}z $
if yes, how ...
1
vote
2answers
169 views
Adding multiple Complex Numbers in Euler form
Say I have a series of $n$ complex numbers of the form $A_k e^{(I \ \theta_k x)} $ where $A_k$ is a real number and so is $\theta_k$ and $k$ runs from $1$ to $n$. $x$ is an algebraic symbol.
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0
votes
3answers
436 views
Solving cubic equation for real roots
I'm looking to solve the following cubic equation for x:
$\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this ...
1
vote
1answer
327 views
Forcing FindRoot to return only real solutions
FindRoot documentation reports that if the Equation and the initial point are reals, the solutions are searched in the real domain.
However, in the following case I ...
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 ...
0
votes
1answer
101 views
Manipulate[]'ing complex roots of an equation using a 2D slider [closed]
I want to make a demonstration of how the complex roots of a polynomial change when I alter the coefficients. Here is my attempt:
...
3
votes
3answers
169 views
Show does not combine the plots
i've the following problem:
because it's not possible to plot complex numbers (or is it?) i created my own "function":
...
0
votes
1answer
107 views
Why am I not getting Indeterminate for f[1] when f[x_] = (x - 1)/(x - 1)? [closed]
In Mathematica 9 If I write:
f[x_] = (x - 1)/(x - 1)
I get
1
And if then I write:
...
8
votes
3answers
329 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 ...
3
votes
2answers
438 views
Linear equation with complex numbers
I have to solve an equation of the type $$a z+b \overline{z}=c$$ with $a,b,c\in\mathbb{C}$.
My approach is to set $F(z)=a z+b \overline{z}-c$ transform $z$ to $x+i y$ and then get a real linear ...
3
votes
1answer
304 views
Bifurcation diagrams for multiple equation systems
I am interested in constructing a bifurcation diagram for some of my parameters (especially for β and γ) in the dynamical system given in the code below. I want to see how parameter changes affect the ...
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 ...
3
votes
1answer
104 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"]
...
8
votes
0answers
100 views
7
votes
2answers
224 views
Moving the location of the branch cut in Mathematica
According to the documentation, Mathematica chooses the branch cut for $\log(z)$ to lie along the negative real axis. It it possible to change this so that it lies along the positive axis or elsewhere ...
1
vote
0answers
151 views
Function approaching incorrect limit in mathematica [closed]
I am interested in the complex function
$f(z)=\frac{1}{a}\log\left[2\sinh(a\sqrt{z})\right]$.
where $a > 0$ is a real parameter. Clearly for large $a$ this approaches $f(z) \to \sqrt{z}$.
But ...
2
votes
2answers
303 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 ...
7
votes
1answer
148 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, ...
7
votes
1answer
233 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
...
7
votes
0answers
277 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
votes
1answer
326 views
Symbolic integration in the complex plane
Context
While answering this question, I defined (symbolic and numerical) path integrations as follows
...
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 ...
6
votes
1answer
309 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
308 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 ...
