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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0
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1answer
20 views

NDSolve for complex variables

I am trying to simulate a multiple pendulum system with damping as follows: ...
0
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1answer
39 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
votes
3answers
148 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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2answers
156 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: ...
1
vote
1answer
67 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 $t$, ...
2
votes
1answer
230 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 ...
0
votes
1answer
54 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
votes
3answers
128 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 ...
3
votes
1answer
247 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. ...
1
vote
0answers
144 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
vote
1answer
125 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 ...
1
vote
2answers
107 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 ...
1
vote
1answer
84 views

A simplification of a complex expression

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

Compiling LinearSolve with 2 complex matrices, possible bug

Take two complex matrices depending on one variable, for example: ...
3
votes
0answers
78 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 ...
3
votes
1answer
115 views
2
votes
0answers
27 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
votes
1answer
94 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, ∞}], ...
0
votes
0answers
62 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 ...
0
votes
0answers
14 views

Find a conformal map from disc onto trapezoidal plate [migrated]

how can conformal mapping a disk into a trapezoidal plate with defining favorite central point?
8
votes
2answers
155 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 ...
3
votes
1answer
86 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 ...
0
votes
1answer
79 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 ...
8
votes
1answer
139 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: ...
0
votes
2answers
101 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 ...
0
votes
0answers
71 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
votes
0answers
38 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 ...
6
votes
2answers
1k 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 ...
28
votes
1answer
3k views

How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
1
vote
2answers
231 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{...
1
vote
1answer
67 views

Using NSolve for Elliptic Equations over Fundamental Parallelogram in Complex Plane [closed]

I'm considering solving elliptic functions over a fundamental domain of the torus with half-periods $\omega_{1}=\pi/2$ and $\omega_{2} = \pi \tau /2$, where $\tau$ is the modular parameter of the ...
10
votes
1answer
119 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 ...
3
votes
3answers
130 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: ...
0
votes
1answer
34 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
votes
1answer
500 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 ...
5
votes
3answers
256 views

Complex limit gives wrong answer

I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...
1
vote
0answers
240 views

A power series expansion [closed]

Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
1
vote
2answers
95 views

Plot values of an $m\times n$ matrix on the complex plane with color varying along $m$

Let's say I have a complex valued matrix $\begin{pmatrix}1+I&2+2I&3+3I\\4+4I&5+5I&6+6I\end{pmatrix}$ represented by a list: ...
-1
votes
1answer
85 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} : ...
0
votes
3answers
59 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
votes
1answer
64 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
votes
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 $2\pi$ : ...
1
vote
1answer
64 views

How to find the pole of a equation where the residue exist?

I want to calculate the residue of an equation, such as: equ = 1/((x - 2)Sqrt[x - 1]) So first I need to find the pole of the equation. My method is find the ...
0
votes
3answers
82 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
votes
0answers
71 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 ...
1
vote
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 ...
3
votes
1answer
109 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
votes
2answers
182 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 ...