Questions tagged [complex]

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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374 views

Expansion for Modified Bessel Function Around Infinity

I'm somewhat new to Mathematica, and I don't understand why I'm getting inconsistent series expansions for the modified Bessel Function of first kind near $x=\infty$. First problem: I get different ...
6
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63 views

Where is the mistake in computing the particular eigenvector of the following DFT Matrix?

I have the following matrix (the DFT Matrix for N = 3) $$W = \frac{1}{\sqrt{3}}\begin{pmatrix} 1 & 1 & 1 \\ 1 & e^{-\frac{i 2 \pi}{3} } & e^{\frac{i 2 \pi}{3} } \\ 1 & e^{\frac{...
5
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159 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
4
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0answers
119 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
4
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64 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 ...
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53 views

Is `InverseMellinTransform` unaware of second Barnes lemma?

Consider evaluating ...
3
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3answers
466 views

Plot a specific branch of a multi-valued complex function

Let's say I want to plot a branch of the following function $f(z) = \sqrt{z(z-1)}$. Let $z = r_1 e^{i\theta_1}$ and $z-1 = r_2 e^{i\theta_2}$. How can I tell Mathematica to plot the branch for which $...
3
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0answers
109 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}] ...
3
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0answers
655 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: ...
3
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0answers
680 views

Taking real and imaginary parts of indexed functions and speeding up ComplexExpand

I am setting up a large system of ODEs and in order to use the IDA method (which is sig. faster for my system and thus attractive), I must split my equations into real and imaginary parts. I am ...
2
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0answers
38 views

Better way to treat branch cut problem in Mathematica

Currently, Mathematica treats function which has branch cuts; $\log(z)$,$\sqrt[n]{z}$, etc, by taking its principal value. This may cause a problem in Contour integration when the path of integration ...
2
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0answers
155 views

Speed up Mathematica's Simplify and ComplexExpand functions

I am trying to simplify an expression and taking the real part only. However Mathematica use ages to run the command (if it is able to do so in the end). The problem is that the expression I am ...
2
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0answers
33 views

Specifying different thickness for each graded contours of Mandelbrot Set so that I can export it as .STL file.

I am using Mandelbrot Set function in Mathematica to get the Mandelbrot plot. I want to 3d print this model, so want to specify thickness for each contour and then convert into .STL file. Is this ...
2
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0answers
128 views

Integral on unit disk of a function with two singularities

The goal is to prove, using Mathematica, that for $\mathbb{D}$ the unit disk and $u,v \in \mathbb{D}$, $u \neq v$, $$\frac{1}{\pi} \int_{\mathbb{D}} \frac{\mathrm{d}^2z}{(z-u)\overline{(z-v)}} = \ln(1-...
2
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35 views

Linearity of the Conjugate operator

The output of Grad[Conjugate[x + y + z], {x, y, z}] is ...
2
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0answers
57 views

How MandelbrotSetBoettcher function is computed?

Boettcher function is a solution of Boettcher's functional equation, so in case of complex quadratic map: $B(f(z)) = (B(z))^2$ where: B is Boettchers function f is complex quadratic map There is a ...
2
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23 views

`FunctionDomain` working with real part

Is there any reason why Mathematica evaluates the following FunctionDomain[Re[((I + 1) x)], x] (* False *) as False, where I'...
2
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0answers
68 views

Amplitude of a transfer function

I'm looking to calculate the amplitude of a transfer function which is defined in a symbolic way : T=(1 + 2 I r λ)/(1 - r^2 + 2 I r λ) I try this, i doesn't work ...
2
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0answers
79 views

How to ComplexExpand Jacobi elliptic functions?

It seems that Mathematica cannot expand Jacobi $\text{sn}, \text{cn}, \text{dn}$ functions. For example, A&S 16.20.1-3 say that for real $y$ $$ \operatorname{sn}(i y \mid m) = i\operatorname{sc}(y ...
2
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0answers
103 views

Weird behavior of PolyLog

I have asked Mathematica (11.1.0.0) to calculate Sum[Log[n]/n (-9/10)^n, {n, 2, ∞}] This is the sum $\sum_{n=2}^{\infty}\limits\frac{\log n}{n}\left(-\frac{9}{10}...
2
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0answers
283 views

Padé approximation of a complex function

I have an interesting problem for the Mathematica. I have some function, let's call it $G$. This is function of discrete set of equidistant points on imaginary axis, $i \omega_n$, so the typical data ...
2
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0answers
297 views

Using Arnoldi Method with Multiple Options

I have a matrix with many complex eigenvalues, but I only need a few near a particular complex number. I am only looking at the imaginary parts, so I need the few closest on the imaginary scale to my ...
2
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0answers
151 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
2
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0answers
88 views

The number of real values assumed by combinations of complex roots of a decic

Define complex conjugate as the pair of complex numbers $a+bi,a-bi$. Assume you have 5 such pairs and they are the 10 roots $x_i$ of a 10th-deg equation with integer coefficients. In general, how many ...
2
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0answers
421 views

Simple contour integral with a parameter gone wrong

Bug introduced in 7.0 and fixed in 7.0.1 I run into the following problem, I tried to evaluate a very simple integral: ...
1
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0answers
32 views

How to compute Bott-Chern operator ddc

I wish I could make Mathematica compute the $dd^c=2i\partial\bar\partial$ of a function depending on several complex variables. The question involves complex or Wirtinger derivatives (https://...
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71 views

How can I get Mathematica to recognize that $ab^* + ba^* = 2\Re(ab^*)$?

Mathematica understands that $z + z^* = 2\Re(z)$, FullSimply[z + Conjugate[z]] (* output: 2 Re[z] *) However, Mathematica does not simplify the expression ...
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0answers
31 views

Discontinuities in taking the roots of a complex function

I have the following functions e1, e2, and e3 which consists of the functions ...
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0answers
63 views

Efficient evaluation of real/imaginary parts of long expressions

I have the following, rather compact, but complex, expression (see below). I simply want the real part of this. Now, when I do the usual, i.e., ...
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0answers
36 views

Inverting a series

How do I invert the following, \[Rho]=r + b0 Sum[Pochhammer[1/2, k]/(k! ((1 - q) k - 1)), {k, 0, \[Infinity]}] + b0^(1 - q)/(2 q) r^q + O[r^(2 q - 1)] to get $r(...
1
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0answers
77 views

Is there a way to reduce size of complex number?

I would like to create huge matrices with hundreds of thousands of elements per side and I would like to use complex numbers in it for further processing by Mathematica functions. When I investigate ...
1
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0answers
269 views

How to graph this function's Riemann surface with Mathematica

I was studying Riemann surfaces, when I found this fancy plot Sadly the only specification of the figure was this miser caption Riemann surface for $$W(z)^{d}+W(z)+z^{d-1}$$ with $d=5$ where $W(...
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0answers
54 views

CountRoots[] won't count my roots. Can I force it to?

I have a big messy function consisting of lots of combined Bessel and Hankel functions that I want to count the roots of. Mathematica doesn't want to try though because it can't prove the function is ...
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0answers
70 views

Very slow Absolute value computation (Improvement need)?

I have to compute the following absolute value. When computing the absolute value of the two pieces separately, everything works fine. When summing up and then evaluating the Abs of the Sum, the code ...
1
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0answers
124 views

Showing Cosh(I x) and Sinh (I x) rather than cosx and sinx?

The following code gives a function expressed in terms of sines and cosines. How to get the analogous with sinh and cosh, coming from the identities: sinx=sinh(Ix)/I and cosx=cosh(Ix)? ...
1
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0answers
723 views

Invalid integration variable or limit(s), for a complex function

I am a beginner in Mathematica. I'm wondering if Mathematica could do the integration of a complex function and plot the values in a 3D graph. Here is the code. ...
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0answers
53 views

Different Derivative's output with ComplexExpand

Consider this expression f = Abs[ x + I ] with this assumption $Assumptions = Element[x, Reals] Now there is something ...
1
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0answers
183 views

Manipulate Parametric Plot of Complex Function

I have a complex function that I would like to understand better using Mathematica's graphing capabilities, but I'm not having any luck with using "animate". The function I am studying is defined as ...
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0answers
79 views

Instructing DSolve not to return answers with explicit complex numbers

DSolve sometimes returns solutions containing explicit complex numbers, even though the ODE does not. For instance (drawn from question 126072), ...
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0answers
93 views

Circularly multiplying a bitmap image

I would like to do the following: 1) Take an image inside a circle and a radius of the circle, and imagine that there are 2 copies of the radius like the handles of a Japanese fan fully opened to 360 ...
1
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0answers
249 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
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0answers
87 views

Interval arithmetics and complex numbers

I am trying to do some simple calculations for a computer assisted proof and since they are not too demanding I thought of using Mathematica. I seems that Mathematica is great for interval ...
1
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0answers
187 views

How do I calculate this integral along a complex line (not a contour) in mathematica?

Given the function: $$f(z) = \frac{\pi ^2 \cot(\pi \sqrt z) \cot(\pi \sqrt {z-a})}{4\sqrt{z^2 - az}}$$ Where a is a positive constant and: $$z = \frac{i}{b} + t $$ $$t>a$$ Where b is also a ...
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0answers
80 views

Finding consecutive residues of large expression?

I have given a large expression expr (has LeafCount of 2772, you can find it in this file or ...
1
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0answers
271 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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0answers
112 views

Complex input for Compile makes it slow

I asked a question here and then tried to use Compile for the solution to gain even more speed. Inside Compile there is a loop ...
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0answers
813 views

Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form $$\left\{ \begin{align} i\frac{da_1}{dt} &=...
1
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0answers
81 views

Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
1
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1answer
111 views

Simplification is not working properly for Complex functions

I have a Matrix whose eigenvectors are needed to be calculated and then I have to calculate the Projector out of it. But due to some unavoidable(atleast up to now), I am not able to carry out the ...
0
votes
1answer
57 views

How to substitute by NDSolve solution to plot a new function

Assume I got some function by NDSolve , like y(t) ...