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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34 views

Invariant curves of complex functions

How to draw automatically the invariant curves of a complex function in the complex plane? And on the Riemann sphere?
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3answers
94 views

My evaluation is taking a lot of time

I was evaluating the roots of a transcendental equation, when I noticed that Mathematica never finishes but stays in the running state. The following is the code that I was using: ...
2
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0answers
33 views

Solving a differential equation with a complex (independent) varible

I'm trying to plug in complex values in the numerical solutions of ODEs without success. For instance y[I] /. NDSolve[{y'[x] == 0, y[0] == 3}, y, {x, -10, 10}] ...
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1answer
95 views

How to solve coupled complex-valued equations faster and get simplified solution

I have six coupled equations. How to solve these equations symbolically faster in Mathematica. In these equations, variables p,q,x,y are ...
4
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1answer
48 views

Returning all branches of a multiple-valued function

This question and answer was inspired by this closed as duplicate question. One possible definition of the n-th order root of x ...
2
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1answer
43 views

Derivative of conjugate multivariate function

I have a problem with Mathematica, taking the derivative of the conjugate of some function. I know that a similar question has been posed before here, but the solution did not work for multivariate ...
2
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1answer
50 views

Mathematica does not distribute conjugation when used with Assuming sometimes?

If I input: Assuming[$x_{-} \in$ Reals, FullSimplify[Conjugate[$e^{i x_1}x_2$]]] Then the output is: $e^{-ix_1}x_2$ As it should be. And if instead I do: Assuming[$x_{-} \in$ Reals, ...
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0answers
46 views

How do you force Mathematica to list all values of some multi-valued complex function at some point? [duplicate]

Let's say I have a complex-valued function $f(z) = \sqrt{z}$. When I plug $z = 1$ into it, it returns 1. I need it to return a list $\{-1,1\}$. Is it possible to force Mathematica to do that? I know ...
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0answers
21 views

Plotting a dispersion curve with complex wavevectors [duplicate]

I want to reproduce a dispersion curve from P. Zou's thesis found here: http://www.ipd.anl.gov/anlpubs/2001/06/39620.pdf on Pg. 31, Eq. 2.13. The problem is, the code below only gives values for the ...
4
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2answers
97 views

Reading from a file: complex number with small imaginary part

I'm trying to read a matrix from the next file: 1+1e-18i 24 42 23.43e-23i using u=Import["file.dat","Table"]; and then find, ...
2
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0answers
93 views

Evaluating Real and Imaginary parts in a dispersion equation via ContourPlot [closed]

I want to reproduce a dispersion curve from P. Zou's thesis found here: http://www.ipd.anl.gov/anlpubs/2001/06/39620.pdf on Pg. 31, Eq. 2.13. The problem is, the code below only gives values for the ...
4
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2answers
528 views

Order of a pole

Is there a simple way to determine the order of the poles of a rational function? I have a difficult function where I need Mathematica to find the poles. It would be interesting to also know what the ...
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0answers
35 views

Graphing imaginary numbers [duplicate]

I'm solving [Sum(i=1..p) x^i] = 100. The max value of 25 is arbitrary. I would like to see how the solutions look in 2-dimensional space. How do I view an imaginary number on a Cartesian coordinate ...
0
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2answers
37 views

Equality of expressions containing complex numbers [closed]

I am using Mathematica to test the equivalence of symbolic expressions. I run into what appears to be a bug when I test the equivalence of expressions involving an imaginary number taken to a complex ...
0
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2answers
75 views

Summing complex numbers

Maybe it is a very stupid question but I am having trouble with summing complex numbers in Mathematica. I have q = l1 E^(2 π I t1) + l2 E^(2 π I t2) where ...
3
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2answers
121 views

How to declare a function as real in order to get rid of Conjugate in front of the expressions?

I have a complicated complex function containing some other ones that are real, f=f(A,B,C,...) ,where A=A(r) and it is real, for ...
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0answers
39 views

Please explain this unexpected code snippet behavior [duplicate]

Consider a function that maps a complex function z->f(z) to it's multivariable counterpart (x,y)->f(x,y) ...
3
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1answer
169 views

Factoring the imaginary unit

Suppose you have this: Collect[2 u + I + 2 + I,I] It gives the same. Is it possible to factor I in elegant way (not ...
3
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0answers
51 views

Why does FreeQ seem not to work with complex numbers?

I guess I do not understand how Mathematica evaluates this simple expression inside FreeQ ...
2
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2answers
119 views

Plotting a set of points given by a complex expression [closed]

A have the set consisting of the complex numbers $1+3r \cosθ−ir \sinθ$, where $r∈[0,1]$ and $θ$ may vary between $0$ and $2π$. This is my first encounter with Mathematica, and am having difficulty ...
7
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1answer
91 views

How to calculate residues using different branches of the logarithm

My goal is to be able to compute the residues of something like $z^{\alpha} R(z)$ where $0 < \alpha < 1$, $R(z)$ is rational, and the exponential can be chosen with any branch. I found a way to ...
4
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2answers
158 views

Analytic expression for a Complex Hilbert Transform in Mathematica

I need to solve the following integral equations for a problem I'm working on - $\frac{-i}{2 \pi}$ $\int_{-a}^{a} \mathrm{dt}\,\, \frac{e^{i k t}}{t + i \tau}$ and $\frac{-i}{2 \pi}$ ...
2
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1answer
136 views

How can I find all solutions of a complicated expression in a desired interval with Mathematica?

I have an expression which is a combination of Bessel functions: ...
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0answers
74 views

Plotting Real and Imaginary parts of Riemann Surfaces

I'm working on a project where I need to take curves like, for example, $y^{2}=(x^{2}-1)(x^{2}-3)$ and plot their real and imaginary parts. More specifically, let $x$ just be real and then plot ...
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3answers
82 views

Plotting complex function

(9 Tanh[x]^8 (1 - 2 Tanh[x]^2)^2 (1 - Tanh[x]^2))/(1 + 3 I Sqrt[2/13])^2 How can I plot the function with the range of x {-10,10}?
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2answers
153 views

Drawing contour integral diagrams

I am $\TeX$ writing notes on complex analysis, I need to use figures of contour paths to integrate on them, how can I plot them on Mathematica, something like this adding also the $\gamma_R$ ...
2
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1answer
70 views

Wrong result after Simplify of a complex variable with assumptions satisfying an inequality

Using Mathematica 10,Simplify[a\[Conjugate], Assumptions -> {(a + a\[Conjugate]) > 0}] returns a, i.e. treats ...
3
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0answers
93 views

Discrepancy in the series expansion of $\log(z/(z-1))$ in Mathematica 5

When I calculate the series expansion of $\log\frac{z}{z-1}$ around $0$ in Mathematica 5.2, I obtain: ...
0
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1answer
78 views

Applying ReplaceAll to I (imaginary unit) [closed]

Why does I/.I->-I return -I but Exp[-I]/.I->-I yields ...
0
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1answer
44 views

Compute and Plot the element of a complex sequence

I'm new tho mathematica. I have a complex sequence ${z_n}$ with $z_0:=c$ $z_{n+1}=(z_n)^2+c$ for all $n\in N$ where c is some complex number, I need to plot the first 20 terms of this sequence ...
0
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1answer
72 views

Conjugate of I \[Phi] [closed]

I have a bigger expression of which I have to take the conjugate. But this is in itself perplexing. When I write ComplexExpand[Conjugate[I\[Phi]]] I just get ...
0
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1answer
56 views

Plotting the image of a curve under a complex polynomial using Mathematica

I would be able to plot the image of a curve (say the circle with radius $1$ centered at $1+i$) under a complex polynomial (say $p(z)=z^2$) using Mathematica. I know how to find the level curves of ...
5
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1answer
179 views

How to plot the solution of a Partial Differential Equation?

My attempt. I need to solve numerically the Complex Ginzburg-Laudau Equation (CGLE): $$ \frac{\partial A}{\partial t}=\epsilon A-(1+i\beta)|A|^2A+(1+i\alpha)\nabla^2A $$ I'm using a uniform initial ...
9
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1answer
185 views

Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
1
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0answers
90 views

Real part of a sum

I would like to take the real part of the following expression: Sum[(a[i] + I b[i]) r^i/(r^2 + z^2)^i, {i, 0, 2 n}] where all of ...
1
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1answer
288 views

How to plot the graph of the equation F[x,y]=0 if y is real number, x is complex? [closed]

I have an equation F(x,y;a,b,c,...)=0, where x and y are variables, a,b,c,... - parameters. y is a real number, x - complex. For every given y I need to solve this equation, i.e. to find Im(x) and ...
1
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2answers
163 views

Complex numbers from two arrays with Real and Imaginary parts

I have two arrays, containing the real and imaginary parts of a list of complex numbers. Re = {{Re_number1},{Re_number2},...} Im = {Im_number1},{Im_number2},...} ...
0
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1answer
57 views

How to get the modulus of following complex number

I want to get the modulus of following (1+(x+I*y)/2+(x+I*y)^2/12)/(1-(x+I*y)/2+(x+I*y)^2/12) I use ...
1
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1answer
109 views

Polar color coding for complex function plots?

Having browsed this Q on plotting complex functions and the Zeta page, I don't see anything as nice as this plot from Matilde Marcolli's slides "Geometry and physics of numbers". Looks like ...
8
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2answers
200 views

Strange behavior of Limit in Mathematica 9 and 10 (bug?)

fixed in 10.1 Consider a complex logarithm where the branch cut is defined along the negative axis. Then for $r$ and $\eta$ real and positive we can write $ \lim_{\eta \to 0} \log(-r+ i \eta) = ...
5
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3answers
720 views

Complex conjugate

How do I complex conjugate a vector? ...
2
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1answer
157 views

Working with derivative of conjugate of a complex number

I have a complex function, lets say $g(x)$. I want to take its and its conjugate's derivative. I need the solution of derivative which must be symbolically and computationally efficient. Lets take an ...
1
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1answer
63 views

Factor bivariate polynomial over the complex numbers

This is very much like Factoring polynomials to factors involving complex coefficients except that I'm concerned about bivariate polynomials, not univariate polynomials. Take for example the ...
1
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2answers
257 views

How to calculate the phase spectrum

I have the following frequency characteristics in the Fourier domain: $$H(\omega)=\frac{-\omega^2}{63170s^{-2}-\omega^2+355.1s^{-1}i\omega}$$ How do I find the phase spectrum from this? I should ...
0
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2answers
61 views

For the same function, why does /. give a complex result?

I define a very simple function like this, g[k_] := 1. + 2 Sum[1/(1 + (2 n)^2), {n, 1, k}] g[50] give the result is: 1.70279. But g[n] /. n -> 50 give aother result: ...
0
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1answer
67 views

Optimizing complex functions

I am trying to optimize a function containing complex numbers, however I keep running into errors. Consider the simple optimization problem: ...
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1answer
96 views

How to obtain Laurent series coefficients of an (almost) arbitrary function?

I have observed that Series in Mathematica assumes that the given function is smooth in the point around which one wants to perform series expansion. For instance: ...
9
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3answers
124 views

Pattern matching with Complex. Feature or a bug?

fixed in 10.1 (windows) I have run into some strange behavior while doing some pattern matching. First, this works as expected: ...
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1answer
116 views

Plotting Complex Numbers - Functions of Complex Numbers [duplicate]

So I have to generate a few different plots with z, where z is a complete number... z[x_, y_] := x + y*I F[z_] := (25*Pi*z*I)/(1 + 10*Pi*z*I) First, I need to ...