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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42 views

How to find function existence border

I have a function like this f[x_, a_] = Log[-x - a]*(-x - a) + Sin[a]; this function does exist if x > a because of Log[]. a - parameters. if I plot a few graphs ...
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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 ...
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1answer
49 views

How can I plot an exponential Fourier series? [closed]

Iam triying to plot summatory of the next function: (e^(i*n*t*wo)*Sin[n*Pi/2])/(n*pi) I have no problem plotting a trigonometric fourier serie, so the only ...
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1answer
33 views

Distribute Conjugate over expression?

I have this output: Conjugate[Subscript[a, 0][x] + t^\[Beta] Subscript[a, 1][x]] I want to distribute Conjugate: ...
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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: ...
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3answers
94 views

ploting the graph of 1/z for a given value

I want to plot the graph of ${1}/{z}$ , for a specific single value of |z| (z - complex variable) . I would like something like ...
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0answers
53 views

Using DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
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0answers
36 views

How to specify in NDSolve that the sought function is holomorphic?

If I include the Cauchy-Riemann equations condition in complex form for the sought holomorphic function gf in NDSolve like this: ...
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2answers
90 views

Plot a line on the complex plane knowing one point and its orientation

I want to draw a line on the complex plane which begins at $0.4+0.1i$, and with an angle of $\frac{\pi}{4}$ with respect to the real axis. Is there a simple way to do this in Mathematica?
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1answer
293 views

Branch cuts of sqrt

I was trying to plot some complex functions with branch cuts on mathematica but I have two problems. 1) The function is with z-Sqrt[z-1]*Sqrt[z+1] with z complex. Now Mathematica says that the ...
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1answer
140 views

Why does Compile not make my function faster?

I need to speed up a large program that repeatedly calls the module below (I've not trimmed the code for this question to ensure there is enough calculation to show a speed improvement.) The obvious ...
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1answer
75 views

Simplify Re[z] in equation to more “natural” form [closed]

If you have a triangle in the complex plane with vertexes {a,b,c} (all complex numbers), the length of the altitude from A to the side BC can be computed as: ...
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2answers
110 views

How to plot list of numbers in the complex plane? [closed]

This should have a trivial solution, but how do I plot a list of (complex) numbers in the complex plane? Or, put another way, why doesn't the code below work? I get the error "... is not a list of ...
7
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1answer
88 views

Why can't I replace I with HoldPattern@I?

Just try this sample: I /. HoldPattern@I -> a (* I *) Why does it fail to replace I with ...
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2answers
102 views

How to plot in the complex plane? [duplicate]

I am new to Mathematica and I would like to ask how to plot in the complex plane in general. Also, as an example, how do you plot $e^{i\theta}$ in Mathematica? In physics the function $e^{i\theta}$ is ...
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3answers
179 views

How to tell Mathematica to get the real-only inverse function?

The problem I have is that Mathematica seems to play better with complex numbers so that the result of N[InverseFunction[Function[x,x^3]][-1]] is ...
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3answers
75 views

replacing complex numbers

I know: I'm going to make a poor showing, but really I can't understand this: a is an expressione whose FullForm is ...
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2answers
109 views

Imaginary part of complex number, nothing works?

I want to find the imaginary part of the complex number (a+i*b). say I have a function in the following form: ...
3
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1answer
86 views

Is there a simple way to get the Conjugate of a complex term, provided all information is available?

I've found a few threads addressing this, but they all seem to have pretty clunky answers, and it's hard to believe there's not a more elegant solution in Mathematica: Remove annoying Conjugate a ...
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3answers
444 views

Solving complex equations with variable exponents

How would I go about solving $(1+i)^n = (1+\sqrt{3}i)^m$ for integer $m$ and $n$? I have tried ...
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1answer
64 views

3D-plots of Complex-parametered trig-functions returns empty plot

I first tried to plot a parametric equation as follows; ...
2
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1answer
83 views

Can't obtain Real results using NSolve

I am trying to find the critical properties of the Carnahan-Starling equation of state, $$p=\rho R T\frac{1+b\rho /4+(b\rho/4)^2-(b\rho/4)^3}{(1-b\rho /4)^3}-a\rho^2$$ using this system of equations, ...
2
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3answers
115 views

Contour plot of the imaginary portion of a function given the real part is positive

How do I plot the imaginary part of the function while its real part is positive? For example, for the below code I could have the imaginary part but I am not able to find the positive or negative ...
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1answer
106 views

Solve this equation explicitly for $\beta$

Solve this equation explicitly for $\beta$: $$T_{12}=\frac{x_{11}+x_{22}}{1+|\beta|^2}\beta$$ $x_{11}$ and $x_{22}$ are positive real numbers where $x_{11}>x_{22}$ and $T_{12}$ and $\beta$ are ...
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2answers
94 views

Simplify complex square roots

I want to simplify the following expression as follows: $$\sqrt{\left(\gamma -\kappa _2\right){}^2-16 G_2^2}=i\sqrt{-\left(\gamma -\kappa _2\right){}^2+16 G_2^2}$$ I am trying ...
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2answers
58 views

Unable to simplify the real part of a complex expression

Simplifying this expression shouldn't be hard. I tried adding assumptions asserting that all involved variables are real, but still the Re expression remains ...
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2answers
70 views

Complex polynomial variable transformation

I have two real polynomials that depend in variables (xi1, xi2) and parameters (eps, e2). I apply the following complexification:...
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1answer
56 views

Why doesn't a real variable's conjugate evaluate to itself?

I have this code (it's just a snippet to exemplify my issue): Assuming[Element[a, Reals],Conjugate[a]] Which results in the output: ...
4
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1answer
92 views

Fitting real and imaginary parts of a function

I have an analytic form of a function G[w_] = -I*z0*w/(1 + I*z0*w*a) I know this function can be obtained (up to some overall normalization) from solving a ...
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0answers
123 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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2answers
91 views

Expression containing $\tt{I}$ is real — how can I show this is so in my notebook?

When I solve this equation (for ϕ): -16 y - (1 + 2 ϕ)^2 (-1 + 6 ϕ) == 0 Two solutions have imaginary parts in the symbolic ...
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2answers
89 views

Display the list of complex roots returned by Solve in their polar form [duplicate]

If I input: Solve[z^4 == 2 (Cos[2 Pi/3] + I Sin[2 Pi/3])] Mathematica returns: ...
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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 ...
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1answer
61 views

Plotting an expression with a complex-valued exponential [duplicate]

Given the wave function $\Psi\left ( x,t \right ) = \psi\left ( x \right )T\left ( t \right )$ with the spatial component of the wavefunction $\psi(x) = \psi_{0}e^{-ikx}$, I tried ...
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2answers
121 views

How can I draw a hyperbola of a complex form

How can I use Mathematica to draw locus of point in complex plane given by $||z-i|-|z+i||=1.$ I have tried few codes, but not succeed.
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1answer
98 views

Problem with complex conjugation of series data in mathematica 10

ComplexExpand in Mathematica 10 doesn't work with series data: Taylor = Series[Exp[I x], {x, 0, 4}]; ComplexExpand[Taylor\[Conjugate]] gives 1+I x-x^2/2-(I x^...
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1answer
87 views

Integrating sinc function over discontinuity

I would like to analytically integrate the sinc function. First of all, if I just perform the integration the following way, everything is as expected: ...
2
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1answer
88 views

FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
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0answers
69 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 ...
4
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1answer
222 views

Plotting Riemann Surface of $w(z)=\sqrt{1-z^{2}}$

I'm working in the plotting the Riemann surface of two functions, namely: $$ w_{1}(z)=\sqrt{1-z^{2}} \,, $$ and $$ w_{2}(z)=\tanh\left(k\sqrt{1-z^{2}}\right)-2iz\frac{\sqrt{1-z^{2}}}{1-2z^{2}}\,, $...
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2answers
66 views

Translating syntax of a pure function

I have a matrix in complex exponential form. I want to factor out the complex exponential form and then express the inside in the a+i*b form. For example: \begin{bmatrix} e^{i \frac{\pi}{4}} ...
6
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1answer
122 views

What is the reason that $zz^*$ is not written as $ |z|^2$ sometimes?

For a general (complex) number $z$ I sometimes get terms that explicitly writes (for instance) $$2zz^*+|z|^2. $$ I should add that these expressions come from long calculations involving packages (...
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2answers
107 views

Plotting complex functions to find solutions

Is ParametricPlot3D the best way to plot complex functions to find solutions? The algebra for $e^z = 2 i$ tells me that there are infinite solutions at $\frac{\pi}{2} + 2 n \pi$ for all $n \in \...
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5answers
168 views

Non-algebraic equation in the set of complex numbers

The following equation in $\mathbb{C}$: $4z^2+8|z|^2-3=0$ is not algebraic and has 4 solutions : $\pm\frac{1}{2}$ and $\pm i\frac{\sqrt{3}}{2}$. The Solve function in Mathematica only returns the 2 ...
2
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1answer
102 views

Problem with imaginary/real parts of a complex function

I have a problem with this code: ...
5
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0answers
96 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 ...
0
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1answer
187 views

Why does Mathematica give this ArcSin[2] result?

The code N[ArcSin[2]] evaluates to 1.5708 − 1.31696 I but it should be undefined instead because it is on the branch ...
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1answer
108 views

Simplify not working for a real part of a complex expression [closed]

When I try to get the real part of a term, for example: $\qquad \Re\left(\frac{e^{-i k} \left(2 k^2+\pi ^2 \left(-1+e^{i k}\right)\right)}{\pi ^2-k^2}\right)$ Mathematica will output the same thing ...
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2answers
150 views

Problem with Identifying Complex Components

I am trying to isolate out the real and complex terms in a fairly large expression. During the process, I have made several assumptions that last throughout the entire process. ...
7
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2answers
236 views

Confusion regarding the incomplete elliptic integral of the first kind

I am trying to manipulate a conformal map from the half-plane to a square $z \rightarrow w(z)$ defined by: $$ w(z) = \int \limits^{z} dx \frac{1}{\sqrt{(1-x^2)x}} = \sqrt{2} \; F\left(\sqrt{z+1},\...