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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18
votes
1answer
446 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
votes
3answers
56 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
63 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
51 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
votes
3answers
71 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
62 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
votes
0answers
31 views
1
vote
0answers
48 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
votes
1answer
80 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
votes
1answer
106 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
177 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
49 views

ComplexExpand and Arg function [closed]

Why does the command ComplexExpand[Arg[a]] gives Arg[a] instead of 0? Isn't it that ...
1
vote
1answer
47 views

Chop not working [closed]

I am running a function that has a large output in matrix format with small, complex parts added to the numbers- basically a rounding error. I am trying to use Chop to obtain use-able results, but ...
1
vote
0answers
55 views

Artifacts in the solutions of NSolve [closed]

I have (what I think are) some problems with the precision of NSolve. I'm trying to solve this cubic equation: $a f^3(x)-b f^2(x)-c f(x)-z=0$ for the function $f(x)$ and then plot the following ...
-1
votes
1answer
24 views

What does mean |sin(z)|<=1? [closed]

I already know that the magnitude of sin(z) its equal to sqrt(sin^2(x)+sinh^2(y))
0
votes
0answers
40 views
1
vote
1answer
41 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 ...
1
vote
1answer
60 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
1answer
42 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 ...
1
vote
1answer
31 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: ...
1
vote
2answers
85 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: ...
0
votes
3answers
90 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 ...
0
votes
0answers
51 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 ...
0
votes
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: ...
2
votes
2answers
87 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?
7
votes
1answer
259 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 ...
3
votes
1answer
133 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 ...
0
votes
1answer
69 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: ...
0
votes
2answers
96 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
votes
1answer
85 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 ...
0
votes
2answers
90 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 ...
5
votes
3answers
166 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 ...
1
vote
3answers
72 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 ...
1
vote
2answers
85 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
votes
1answer
81 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 ...
4
votes
3answers
427 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 ...
1
vote
1answer
59 views

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

I first tried to plot a parametric equation as follows; ...
2
votes
1answer
76 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
votes
3answers
110 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 ...
0
votes
1answer
105 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 ...
1
vote
2answers
90 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 ...
0
votes
2answers
57 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 ...
1
vote
2answers
66 views

Complex polynomial variable transformation

I have two real polynomials that depend in variables (xi1, xi2) and parameters (eps, e2). I apply the following ...
3
votes
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
votes
1answer
84 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 ...
1
vote
0answers
117 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 ...
0
votes
2answers
88 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 ...
1
vote
2answers
84 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: ...
0
votes
0answers
42 views

Using NSolve for Elliptic Equations over Fundamental Parallelogram in Complex Plane

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 ...
0
votes
1answer
55 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 ...