Tagged Questions

Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.

2k views

Laurent series expansion

Can someone share how to find a Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at zero on the annular disk $1<|z|<2$?
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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 ...
319 views

ContourPlot with parameter

I have an equation for function F[x,y]==0 which first argument x is real and another, y, ...
170 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: <...
278 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 ...
2k views

Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?

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. ...
662 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 ...
369 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 ...
360 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]]` <...
2k 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: ...
238 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 <...
824 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 ...
601 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 ...
4k 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 ...
580 views

Compiling the VoigtDistribution PDF

According to List of compilable functions, Erf and Erfc are compilable functions. However, I want to make a compiled version ...
2k 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?
501 views

Contour plot doesn't look right

I have an implicit function expression ...
428 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. ...
2k 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 ...
5k 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 ...
740 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 ...
209 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: ...
294 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": ...
2k views

Plot3D with coloring based on phase value of f

I'm reading a sample chapter of Visual Complex Functions by E. Wegert. Near the bottom of this page, there is a link "Download Sample pages 1 (pdf, 2.4 MB)" which allows you to read Chapter 2 of the ...
140 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: ...
3k views

How can I convert a complex number into an exponent form

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 ...
2k 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 ...
3k 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 ...
6k views

Plotting complex numbers as 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 ...
705 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"] ...
295 views

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

Consider these integrals: ...
1k 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 ...
478 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 ...