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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2
votes
1answer
49 views

Discolored ComplexPlot ColorFunction [closed]

I have this code. ...
0
votes
1answer
53 views

Complex infinity at a point and division by zero

Edit: I've found out that the book was written for Mathematica 7, which was a pretty long time ago. It boils down to changes in syntax most probably, but simple renaming to lower lettercase does not ...
0
votes
1answer
50 views

Finding the negative real root of in set of solutions under a varying constraint

Suppose I have a function and its derivative like: V = x^3.5 - x*y Vx = D[V, x] I first solve V for ...
0
votes
0answers
29 views

Expanding the complex conjugate of a Mathieu function as a series

In my calculations, I found this equation: ...
1
vote
0answers
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 ...
0
votes
1answer
39 views

Can we make a labelled parametric plot in which the parameter is integer? [closed]

Can we make a labelled parametric plot in which the parameters are integers? I'm just using Wolfram Alpha but could equally use Mathematica Online, and want something like here. I want to plot ...
2
votes
2answers
127 views

How to show that $f(z) = z^2 + 1$ intersects the line through the roots of $f(z) = 0$ in ComplexPlot3D?

I have plotted the complex function $f(z) = z^2+1$ by using the following code: ComplexPlot3D[z^2+1, {z, -5 - 5 I, 5 + 5 I}] However, I want to show that $z^2+1$ intersects the line $\Re(z) = 0$. ...
17
votes
4answers
708 views

Why is (-1.)^2. a complex number

Why (-1.)^2. in Mathematica returns a complex number? It looks like in both C and Fortran it returns 1. Why does Mathematica behave differently than the other ...
8
votes
5answers
12k views

How can I plot the complex graph of $x^x$ in Mathematica?

For example, this Wolfram Alpha query shows this graph: But it does not show the code for plotting it in Mathematica. Plot[x^x, {x, -1, 1}] only plots the real ...
0
votes
1answer
45 views

Complex Exponentials to Trig Functions?

I have an expression expr = 1/2 a E^(-3 I ω t) (E^(3 I ω t)+2 Cos[π x/a]) (1+2 E^(3 I ω t) Cos[π x/a]) Sin[π x/a]^2; expr // TeXForm $\frac{1}{2} a e^{-3 i t \...
0
votes
1answer
113 views

How to plot the complex function $f(z) = z^2 + 1$ in a three-dimensional plot with colouring?

I've noticed that there are different ways to plot a complex function. What I am interested in, is a three-dimensional plot with colouring of the complex function $f(z) = z^2 + 1$. Here is an example ...
3
votes
1answer
213 views

Using Im[] and Re[] Correctly

Hi I just want to check my code is working properly as I am trying to rule out any errors. I'm integrating 4 coupled ODE's that have real and imaginary terms, so I have 8 equations. The section of ...
3
votes
1answer
122 views

Finding the maximum real part of roots

Suppose that I have this problem ...
0
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0answers
83 views

Plot the maximum of the real parts of the eigenvalues of a trancendental equation

Basically I have this matrix ...
1
vote
1answer
72 views

Plotting $f: x + i\,y \mapsto u + i\, v$ with Plot3D and mapping $v$ to color

Mathematica already has ComplexPlot3D that plots ReIm[x, y] against Abs[f(z)] and ...
2
votes
2answers
632 views

Weird result in complex limit

I am trying to evaluate a limit: gamma[w_] = Sqrt[-(u*e)w^2 + I*(u*s)w]; Limit[Re[gamma[x]], {x -> DirectedInfinity[1]}] I calculated the limit by hand, and ...
2
votes
3answers
319 views

Limit of integral gives incorrect output

I'm trying to evaluate $\lim_{e\to 0} \, \frac{i}{e}\int_{\pi }^0 \frac{1-\exp (i e \exp (i \theta ))}{\exp (i \theta )} \, d\theta$ with Mathematica 9.0.1.0 on OS X. However, I get "Undefined" for ...
7
votes
2answers
242 views

Possible bug with contour integration

I wanted to confirm the value of the integral $$\frac12\int_{\partial\Bbb D}\frac{\sin z}{\cosh z-1}\, dz$$ where $\partial\Bbb D$ is the boundary of the disk of radius $1$. Thus I had written the ...
10
votes
2answers
823 views

Why does Arg'[1. + I] return -0.5?

From the document we know that Arg[z] gives the gives the argument of the complex number z. Then how about ...
12
votes
3answers
450 views

Finding and visualization of branch cuts and branch points

Is it possible to determine branch cuts and branch points for complicated functions using mathematica Iam trying to determine the brnach cuts and branch points of this complicated function We have ...
39
votes
5answers
40k views

Plotting Complex Quantity Functions

Trying to plot with complex quantities seems not to work properly in what I want to accomplish. I would like to know if there is a general rule/way of plotting when you have complex counterparts in ...
17
votes
6answers
8k views

Plotting complex numbers as an Argand Diagram

I have the function: $F(\omega) = \frac{5\; - \;i\;\omega}{5^2\; +\; \omega^2}$ When $\omega$ has the values : $\{ -7, -2,\; 0,\; 2,\; 7\}$ How would I plot the Argand diagram in Mathematica? Or ...
-1
votes
1answer
114 views

ComplexPlot3D and essential singularities [closed]

I am trying to understand the behavior of the functions $$ f(z) = e^\frac{1}{z} \qquad \text{and} \qquad \frac{1}{f(z)} = \frac{1}{e^\frac{1}{z}} $$ in the neighborhood of $z=0$. From the power ...
85
votes
5answers
11k views

How can I generate this “domain coloring” plot?

I found this plot on Wikipedia: Domain coloring of $\sin(z)$ over $(-\pi,\pi)$ on $x$ and $y$ axes. Brightness indicates absolute magnitude, saturation represents imaginary and real magnitude. ...
1
vote
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 ...
1
vote
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., ...
0
votes
0answers
24 views

Integrating System of ODE's

I'm trying to integrate the system $$\frac{d}{d z} \left[ \begin{array}{l}{\hat{a}} \\ {\hat{b}}\end{array}\right]=\frac{i \omega}{\overline{c}} \left[ \begin{array}{cc}{\left(\Delta_{l}^{(+)}-1\...
0
votes
2answers
81 views

Result with assumptions contradicts previous result

Without assuming anything on the argument of the complex number inside the Gamma function ...
1
vote
1answer
35 views

Mathematica is not simplifying trignometric functions under Abs although I provide assumptions

I am trying to simplify a simple expression, (1/2)*((-Pi)*Abs[Sin[t]] - Pi*Abs[Sin[t - 2*Pi]] - 2*Pi*Abs[Sin[t - Pi]] + 4) i.e $$ \frac{1}{2} (-2 \pi \...
1
vote
2answers
81 views

Taking absolute value of complex variable

I'm trying to take absolute value squared of certain objects. Say I have y=alpha and I know that |alpha|^2 = alpha*Conjugate[alpha]. How do I take Abs[y]^2 ...
1
vote
1answer
96 views

How to define a complex function with assumptions?

I'm trying to define a complex function to be able to do analytic calculations. Specifically, I want to define a function $A(x,t)$ in the complex plane with argument $\theta(x,t)$ and modulus $R(x,t)&...
1
vote
1answer
64 views

Find roots of transcendental function in regional complex plane

I want to know how many roots does the following equation have and how to solve them all. $f(z)=\frac{\text{sech}(35.0937 x)}{\left(e^{70.1873 x}-1.\right) x} \left((0.\, +0.0235822 i) x^2 \exp \...
1
vote
3answers
85 views

How to take a derivative of a function with a real part taken

Consider f[x_]=Re[x^3] I now take the derivative of this D[f[x],x] and the result is ...
3
votes
1answer
177 views

What does “ Im' ” mean? [closed]

I am trying to take the curl/derivative of the function A. What does " Im' " mean here? Why does Mathematica attempt to take the derivative of the Im function here? ...
4
votes
4answers
196 views

How to find image of a complex function with given constraints?

I am very new to Mathematica. I have started learning it only last month. I would like to graph the image of some complex valued polynomials with some provided conditions. For example: $$ p(z_1,z_2,...
2
votes
1answer
286 views

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

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

Mathematica doesn't extract Re and Im parts properly

I have a code: ...
0
votes
1answer
95 views

Complex number as the result of an integral [closed]

My question has been asked before by other members, however, I didn't find the answer to their question helpful in my case. I'm doing a simple numerical integral with real numbers in mathematica, but ...
6
votes
0answers
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{...
0
votes
2answers
138 views

Numerically integrate complex valued function of a real variable and a complex variable

I need to numerically integrate a complex valued function of a real variable and a complex variable by the real variable. My integral: $$ \int^1_{-1}\frac{e^{ix}}{x-z}dx ~~~\text{where} ~~x \in \...
4
votes
1answer
142 views

Imaginary part of expression too difficult to calculate

I am trying to calculate the imaginary part of a long expression. It's a long enough expression that Mathematica "hangs" when you run: ...
1
vote
1answer
1k views

Plotting a function of one variable in a 3d dimensional complex space

I would like to plot graphs of functions like this: $ f(x)=x^2 +1 $ But in a tridimensional complex space. It should look like this: I am not sure if this has been asked before (Plotting Complex ...
4
votes
3answers
168 views

Conjugate & Derivative

I have some problem with the derivative of the 'conjugate' expression: Here I define the functions: ...
1
vote
2answers
651 views

Plot $\arg(z)$ in an Argand diagram and display the angle

I'd like to ask you about the way to show the $\arg(z)$ annotation about the angle. My point is to show $\frac{2\pi}{3}$ and $\frac{5\pi}{6}$ on the image. What I mean: (source: brocku.ca) Is ...
1
vote
3answers
58 views

How can I reduce my work to get the result automatically?

I want to find the locus of point present of the complex z so that $$|z + 2| + |z - 2| = 18. $$ I tried by hand ...
0
votes
0answers
177 views

Defining a complex partial differential operator

I tried to define a partial differential operator using this code ...
0
votes
1answer
96 views

Can you plot complex maps? [closed]

I want to plot $|z+1|=|z-2+i|$/ Is there any way to do this without converting it to Cartesian form and contour plotting?
0
votes
2answers
82 views

How to Chop parts of an expression?

The following expression has four terms $T1$, $T2$, $T3$ and $T4$, such that the totalFunction = T1 - T2 - T3 + T4;. It turns out that the part T1-T2 gives a ...
7
votes
3answers
231 views

Obtaining a matrix of complex values from associations giving the real and imaginary parts of each element?

I have a list of associations keyed by real and imaginary numbers, like so: ...
9
votes
3answers
722 views

How to use Mathematica to do a complex integrate with poles in real axis?

I want to use Mathematica to compute the following complex integral: Integrate[Exp[I z ] 1/z, {z, -Infinity, Infinity}] Mathematica reports that it does not ...