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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57 views

Complex function plot issue [on hold]

I am plotting the real part of a simple complex function defined in two equivalent ways, and the plots do not agree. ...
0
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1answer
61 views

why the result not contain imaginary, I? [on hold]

Good day, First of all, sorry if my coding in this forum has mistake. I already learned it and this is the best try from me. May anyone help me troubleshoot my problem below. ...
1
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0answers
35 views

Can you define “| |” to be the same as “Abs[ ]”? [duplicate]

When calculating the modulus of a complex number in Mathematica, the standard (and probably least-ugly) way of doing it is by using the Abs[ ] function. When doing ...
0
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0answers
5 views

Meijer's G-function differentiation [migrated]

I am trying to calculate the derivative of the Meijer's G function, Based on wolfram function identities I have found in (07.34.20.0003.01) that the derivative is expressed asl: $\frac{d}{dx}G^{m,n}_{...
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0answers
62 views

solving a set of 10 non-linear system of equations

I have a system of equations and I want to solve it to get a1, a2, b1, ...
0
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1answer
75 views

Cauchy integration [closed]

I am evaluating Integrate[1/(1 + 3*cosin(x)*cosin(x)), {x, -Pi, Pi}] in Mathematica, which should give me Pi, but instead I ...
1
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1answer
49 views

Simplifying x Conjugate[x]

I am trying to simplify a big expression containing many times terms of the form x Conjugate[x]. While this works for a single term: ...
1
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1answer
51 views

NDSolve for complex variables

I am trying to simulate a multiple pendulum system with damping as follows: ...
0
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1answer
50 views

How to make the conjugate transpose

I have a problem to make the conjugate and transpose the matrix.May anyone help me please. ...
3
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3answers
149 views

Simultaneous plotting

For my experiment, I have to simultaneously fit the real part and imaginary part of cavity reflection data which is given here column 1: frequency, column 2: reflection magnitude, column 3: phase I ...
1
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1answer
68 views

Evaluating Bessel-Schläfli-type Integral with Infinite contour

I am attempting to evaluate the integral \begin{equation} \int_{\infty-i\pi}^{\infty+i\pi} dt \frac{e^{-\frac{l}{n}t}}{[(X'-X)^2+r^2+s^2- 2rs \cosh(t)]}, \end{equation} the only variable being $t$, ...
1
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1answer
61 views

Dynamic input for Complex, Determinant output problems [duplicate]

I'm having trouble using Complex with Dynamic real and imaginary inputs. The inputs come from a matrix of popup menus: ...
2
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1answer
242 views

Simplifying square root of exponential

Very simple question: Why doesn't Mathematica simplify this square root expression? Refine[Sqrt[Exp[I p]], p > 0] // FullSimplify It should give ...
1
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2answers
110 views

Factor out imaginary unit of root of obviously negative term

Suppose I have the term $t=\sqrt{-a^2-b^2}$, where $a,b\in\mathbb R$. Of course, we know that it holds $$ t = \mathbb i \sqrt{a^2+b^2} $$ which is (in my opinion) more convenient. How can I get ...
2
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1answer
135 views

Residue failed to reproduce this residue in a paper

This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ...
2
votes
3answers
130 views

NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
1
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0answers
145 views

Problem of calculating the residue of a expression (to confirm the result from a paper) [duplicate]

I use Mathematica to confirm a result from a paper which is to calculate the residue of a expression at zero. The code and result are given below. Is this residue too complicated for Matheamtia or ...
1
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1answer
87 views

A simplification of a complex expression

I use mathematica to confirm a result from a paper ("...
0
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0answers
39 views

Compiling LinearSolve with 2 complex matrices, possible bug

Take two complex matrices depending on one variable, for example: ...
3
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1answer
248 views

Reduce a complex inequality

Reduce[Abs[1/(1 + I/Sqrt[α])] < 0.5, {α}] It is taking long time to run. Can any one help me to get the reduced condition in terms of $\alpha$ or its modulus. ...
3
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0answers
79 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 ...
1
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1answer
72 views
2
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0answers
28 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 ...
0
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0answers
63 views

Why can't Mathematica solve this complex equation?

So I want to find the complex part of Rthev,equate it to zero and solve for ω but it won't let me. Is it because it thinks ...
3
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1answer
120 views

How to calculate this complex expression?

I have a complex expression as follows, ...
2
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1answer
96 views

How is it possible that PolyLog[2,1.1] returns an imaginary number?

Given that: PolyLog is defined as li[n_, z_] := Sum[z^k/k^n, {k, 1, ∞}], ...
3
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1answer
89 views

Complex Plot with Imaginary Part encoded in color

Heyhey, I wanted to plot the complex cosine in a 3D graphic where the real part is given by the surface, while the imaginary part shall be indicated by the color. Therefor, I tried the code ...
8
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1answer
141 views

Symbolic and numeric limit disagreeing on branch cut of ArcTan

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. Investigating comments to my previous question lead me to the following problem: ...
8
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2answers
158 views

Integrate and NIntegrate disagreeing over branch cut of Sqrt?

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. In Mathematica 10.2 I'm trying to integrate this piecewise continuous function, but ...
0
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2answers
103 views

Integral over real valued function becomes complex

I've tried to solve the following integral, but I get a complex solution even tough it should only have a real part. $$f(x)=- \frac{10^{-20} x}{0.99005- e^{10^{-12}x}}$$ Now I want to calculate the ...
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2answers
172 views

Conjugate[a/b + c/d]

Trying to obtain the result of Conjugate[a/b+c/d] only gives the same result. As such, I use Refine as: ...
0
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0answers
74 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_{- ...
0
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0answers
40 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 ...
0
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1answer
85 views

Plotting the modular surface of a complex function [closed]

Tristan Needham stated in the introduction to Visual Complex Analysis that he used Mathematica to create the majority of graphs in his book. I'm trying to recreate the graph he made for figure[14] of ...
1
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2answers
235 views

How to compute this integral?

I'm trying to calculate this integral : $$I(z,k,a)= \displaystyle\int_{1}^{\infty} t^2\, \text{ArcTanh} \left(\sqrt{\frac{t^2-1}{t^2}} \dfrac{k}{z}\right)\, e^{-a\,t} \, dt$$ Where : $\textrm{...
3
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3answers
132 views

How to obtain this expression in terms of real functions

I know that this expression (2 (ArcCot[E^(-((I ϕ)/2)) r] + ArcCot[E^((I ϕ)/2) r]))/π is real, because is the sum of a real series, in particular: ...
11
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1answer
128 views

Definition of Mod and Quotient with complex arguments

How are Mod and Quotient defined for three real/complex arguments? I wasn't able to find the definition. My main surprise so ...
0
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1answer
36 views

Complex number simplifications

My Mathematica notebook is not simplifying some expressions which do look trivial. I mean that one of my outputs contains: ...
18
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1answer
507 views

Numerical inverse Laplace-Hankel transform

When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
0
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3answers
60 views

how to take complex conjugate of a real variable

I have a function defined as follows: g[θ_] := 1/k (Exp[-I δ0] Sin[δ0] + 3 Exp[I δ1] Sin[δ1 Cos[θ] + 5/2 Exp[I δ2 (3 (Cos[θ])^2 - 1)) and I compute ...
-1
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1answer
65 views

Real and Imaginary matrix

I have a 2 by 2 matrix T: {{x, y}, {-y, x}} where x is the real part of some complex number and y is the imaginary part of something complex number. Let's say z1 = ...
0
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1answer
53 views

What makes imaginary parts show up?

If I define a function using alpha[y_, d_] := 2 ArcCos[1 - (2 y)/d] Then if $y$ and $d$ are equal, the result is $2\pi$ : ...
0
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3answers
90 views

Write complex number in terms of absolute value and phase

I have a long vector and some of the values (19 out of 64) are complex. I got them using the Mathematica Rationalize function, so the complex ones are written in the a+bi form. Is there a function I ...
6
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0answers
73 views

Generating OpenCL C code [closed]

I'm trying to make an interactive complex function plotter using OpenCl. So far I can only plot functions that I hardcode into the kernel by hand. I'd like to be able to use ...
3
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0answers
34 views
1
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0answers
49 views

Finding Complex expression [closed]

How do you find a real part of a complex expression? Here is an example of what I am looking for complexExpand[Sqrt[x + I*b]] gives me ...
-1
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1answer
88 views

Image of the unit circle under a complex rational function

Let $$f(z)=\dfrac{z(z-a)}{(z-b)(z-c)(z-d)}$$ be a complex rational function with distinct non zero complex numbers $a,b,c$ and $d.$ I need to plot the image of the unit circle $S=\{z\in\mathbb{C} : ...
3
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1answer
111 views

Calling Integrate with many limits of integration

I accidentally discovered that you can put many numbers into the limits of integration of Integrate and Mathematica will still evaluate it without returning an ...
3
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2answers
189 views

How can I get Mathematica to simplify this i * sqrt expression

In[11]:= FullSimplify[I Sqrt[-1 + w^2], Element[w, Reals], Assumptions -> 0 <= w <= 1] Out[11]= I Sqrt[-1 + w^2] Is it possible to have Mathematica ...
2
votes
1answer
77 views

ComplexExpand and Arg function [closed]

Why does the command ComplexExpand[Arg[a]] gives Arg[a] instead of 0? Isn't it that ...