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.
1,236
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One more incorrect result of FunctionMeromorphic and FunctionAnalytic
Two years ago I submitted a bug in FunctionMeromorphic (That bug still persists in 13.2.). Here is one more incorrect result in it and ...
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50
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1
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2
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Holomorphic derivatives (in 2 d) in Mathematica
In 2 Dimensional Conformal field theory, We have two coordinates $ z=x+i y$ and $\bar{z}=x-i y$. Here $x$ and $y$ are both real. So, one can work directly with $z$ and $\bar{z}$.
I want to define $\...
- 29
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80
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Green function and differential equation
I'm trying find the Green's function for a special operator.
I have the homogeneous equation
x (x - 1) y''[x] - 2 I Zm y'[x] - L(L + 1) y[x]==0
for $x>1$ ...
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Simplify complex conjugation and force joining of exponentials
I define the following piecewise functions.
...
- 451
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How to take the derivative of a function in `Im[]`?
I tried to take the derivative of a long expression containing $\text{Re} \text{Li}_3(e^{2\pi ix})$, the trilogarithm while $x$ is real. Since the real part function is linear ,it should be like this
$...
- 153
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How to get Mathematica to give me a specific alternate form? [closed]
I have a lot of equations of a form similar to
$$\frac{x(\frac{4}{3} + 4x^4)}{(x - \sqrt{\frac{2}{3}}e^{i\pi/4})(x - \sqrt{\frac{2}{3}}e^{-i\pi/4})}.$$
All of these equations can for non-zero ...
- 13
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Simple SDP using Hermitian matrices
I would like to run the following semidefinite program
$$ \textrm{Minimize}\,\, \textrm{tr}\big({AX}\big)\\
\textrm{subject to}\,\, X \geq B_1\,, X \geq B_2\,, $$
where $A$, $B_1$ and $B_2$ are ...
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106
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How to change the styles of Real part and Imaginary part in ReImPlot using ReImStyle?
I have following code,
ReImPlot[(2 + 3*I)*x + (4 + 5 I), {x, 0, 3}, ReImStyle -> {{Dashed, Red}, {DotDashed, Red}}]
This will created the plot that looks like ...
- 471
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Finding real and imaginary part of long expression takes too long
I generally try to find real and imaginary parts of long expressions such as in the following example. But it takes too long time.
a) How can we speed up it? (and it includes terms such as ...
- 355
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1
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DSolve solution for 1st order PDE involving complex number does not match initial condition
Bug introduced in 11.3 or earlier, persisting through 13.2.1.
[Mathematica 12.0.0.0, MacOS X x86 (64bit)]
Trying to solve
...
- 175
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85
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How to compute the residue of $f(z)=\frac{n/z}{z^{n}-1}$ to be $-n$ at $z=0$? [duplicate]
How to get residue of $f(z)=\frac{n/z}{z^{n}-1}$ with correct residue of $-n$ at zero?
It works it out just fine at 1 with:
Residue[(n/z/(z^n - 1)), {z, 1}]
- 333
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3
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305
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Plotting a complex matrix with phase dependent color
I want to plot a complex matrix, i.e., a matrix with complex number entries. I want the matrix to be plotted as DiscretePlot3D as shown in the figure (top figure). But, I also want each bar to be ...
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Mathematica does not accept that this variable is a positive real?
So I have the following expression that derives from previous computations:
...
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1
answer
61
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How to make Mathematica able to integrate $\int_{-\infty}^\infty \frac{e^{ikx}}{(x+ia)^3} dx = i\pi k^2 e^{ka} \theta(-k)$ for $a>0$?
I want to evaluate an integral which is essentially a sum of the form $\lim_{a\to 0^+}\int_{-\infty}^\infty \frac{e^{ikx}}{(x+ia)^m} dx$, where $k\in\mathbb R$ and $m\in\mathbb N$. By the residue ...
- 1,009
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4
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385
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Displaying results with Exp instead of powers
Entering
Solve[z^4 == -1]
gives:
{{z -> -(-1)^(1/4)}, {z -> (-1)^( 1/4)}, {z -> -(-1)^(3/4)}, {z ->
(-1)^(3/4)}}
or $\left\{\left\{z\to -\sqrt[4]{-...
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63
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FullSimplify does not simplify involving `ResidueSum`
Consider the following code involving ResidueSum:
...
- 1,009
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1
answer
89
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How do we separate a complex matrix into real and imaginary matrices?
If we have a complex matrix C, how do we separate it into two matrices as C=A+iB, where A and B are real matrices?
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2
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86
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How to write a Mathematica code to plot complex function in a 3D plane [closed]
f(x)=square(X)+ix. Plot a 3D plane for this complex function
0
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70
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how to draw the roots of a complex number
I created a simple code to calculate roots of a complex number using De Moivre's formula. I would like to draw these elements.
...
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46
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Replace x + I y by z in complex expression
Say I define
z = x + I y;
Then I calculate
-2 Im[z] + 3 + I(2 Re[z]) // ComplexExpand
which gives
...
- 717
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Polar graph of the Riemann zeta function
I would like to plot a complex graph of the Riemann zeta function on the Argand diagram $ς(s)$, where $s = \frac{1}{2} + i t $, and the value of $t$ is varied to get a graph in the polar form.
Can ...
0
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2
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Plotting a complex number on the Argand diagram [closed]
I want to plot (0.25)^(2+i) on the Argand diagram.
Can anyone help me with it?
2
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1
answer
257
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How to calculate infinitesimal analytic continuation?
Many problems in science and engineering are related to the analytic continuation and in particular infinitesimal analytic continuation to the upper or lower complex plane, i.e., a generic complex ...
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How to avoid using the principal branch?
How can I make Mathematica to use $Log[-1]=i\pi+2i\pi*n$ with $n\in\mathbb{Z}$?
Currently, mathematica set $Log(-1)=i\pi$ and when I try to redefine the value of $Log[-1]$ I get the message "Set::...
- 121
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How to plot an imaginary number, i, power tower as done in the following way?
Can somebody explain what two variables exactly they have plotted against each other to get such graphs, and how one would go about getting this graph in Mathematica?
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How to change branch cut of Log[z] to positive real axis, [duplicate]
No one ever answered original ZZZ's question in a straightforward shortest code
" Mathematica chooses the branch cut for log(z) to lie along the negative real axis. It it possible to change this ...
- 309
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1
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121
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How can I plot a list of complex numbers against a parameter while separating their real and imaginary parts?
This is a sort of continuation of How can I make a list of values "remember" the entered parameters?
I have some cubic function which solves for a variable ...
- 89
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173
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How to get the real part of a complex function with some real coefficients?
I want to get the real part of the function n3[t] (see below) which is the solution to a differential equation.
Solve the differential equation. (Suppose ...
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63
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Why do I get different results for this complex line integral?
I want to compute line integral of $f(z) = \frac{1}{z(z-1)^{n+1}}$ over a closed curve $\gamma: t \mapsto 1 + \frac{1}{2} e^{i t}, t \in [0,2\pi]$ in the complex plane in two different ways but the ...
- 153
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Plot circle of radio `r` in complex plane
I am having a brain-not-working day...
Embarrassingly, I can't figure out how to plot a circle on the complex plane with origin z_0 and radio ...
- 2,047
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Converting a complex matrix into an equal-sized PNG
Now, I would think that when I run the following code, I'd get a 20x20 pixel image I could copy as a PNG with all the pixels corresponding to the given(although in this case random) data. Instead, I ...
- 171
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Julia set and external rays for high degree
We know that the soft "Mandel dynamics" by W,Jung give us the way to draw the Julia sets and their external rays, I wonder whether there are good programs for polynomial of high degree, ...
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Finding the equation of a circle for complex numbers
Solve[Abs[z]²==1,z]
returns two solutions, -1, and 1. I would like to get all the solutions of the
form Exp[I c₁].
...
- 193
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FullSimplify not working when simplifying a complex number
Here is a snippet of the code I am working on, which requires me to get the Real part of the Harmonic Oscillator wavefunction.
...
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Solving an equation without output
Could you please help in solving the equation below. I am not able to do it with the current version of mathematica (very old one). All parameters are real and positive.
Thank you so much in advance
<...
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3
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203
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How to get rid of complex terms in the given expression and rewrite it as a real function?
I have an expression exp in terms of the parameter $n\in\mathbb{N}^+$ which takes the values
$n=\{ 1,2,3,4,5,6,7,8,9,10 \}$. As can be seen (a picture is also ...
- 1,159
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What is the most efficient/optimal way to simplify the given function? Does the given code need more assumptions?
I have a very long function for $\{x,b\}\in\mathbb{R}$ and $n=\{1,2,3,4,5,6,7,8,9,10\}$; here, I have only mentioned a short part of that. The function is a sum of the complex exponentials (a picture ...
- 1,159
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91
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How to treat variables in an expression as real? [closed]
Let's say we'd like to define a general complex polynomial and then separate the real terms from the imaginary terms. We could define
...
- 113
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59
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Unable to solve a couple complex valued differential equation usingNDSolve [closed]
I am new to Mathematica and I am trying to use the NDSolve to deal with the following odes
...
- 101
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4
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106
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Simplifying a function to get rid of fractional powers of $-1$
I have the following function for $x>0$.
...
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answers
68
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Showing Real and Imaginary parts of a Complex expression without reordering
I know Mathematica has a strong tendency to reordering expressions, but this is too much and there must be a way. So I'll give you an extremely simple example.
I define this ...
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107
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Solve a system of complex equations with parameters
I have a system of ten complex equations, with four complex variables u1,u2,v1,v2 and two real variables θ1, θ2. In these ...
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Complex conjugate in Mathematica [duplicate]
Suppose $a$ and $b$ are two complex variables, how to realize：
$$\text{Conjugate}[a+b]=\text{Conjugate}[a]+\text{Conjugate}[b] $$
in Mathematica.
Suppose in following situation, I want to simplify:
<...
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80
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Evaluating a complex expression
I have the function complex valued function g[z_]:=(2a z^2+bz)/(az^2+bz) where $z=e^{i \theta}$.I want g in terms of $\cos(\theta)$ and $\sin(\theta)$.How do I do it mathematica?Next I want value(...
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2
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698
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How to prove this algebraic identity?
I mean
$$\forall z \in \mathbb C\left(\ \left| \sqrt{z^2-1}-z\right| +\left| z+\sqrt{z^2-1}\right| =| z-1| +| z+1|\right ) .$$
The command
...
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2
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Checking region membership in a polygon defined by complex roots
I want to define a function that returns True if a complex number $z$ is in complex set $\Omega $ which is the pentagon with vertices located at the fifth roots of ...
- 243
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2
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How to get rid of the absolute value in ComplexPlot3D[]?
I'm starting to study complex analysis,so I'm trying out Mathematica as tool for visualizing complex functions. I'm trying to graph $f(z)=z^2 + 1$ with the code:
...
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287
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Need help with Assumptions for an integral
I want to solve this Log, Integrate[2a Log[-a+((A0 + (y-y1)²)^½, {y1, 0,b}]
But Mathematica only gives me long conditional expressions or imaginary numbers. I (my thinking which can be wrong) assume I ...
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