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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Replicating Complex Plot (branch cuts, poles, shading)
I am trying to recreate the following 2 plots:
where the function being plotted is $|e^{2ipR}S_0^{\text{well}}(p)|$ where $|...|$ is the absolute value, $R=1$, and $S_0^{\text{well}}(p)$ is given as
\...
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Why doesn't mathematica simplify the result of Norm in a Module calculation in this case?
I have a computation that involves the "contraction" of matrix and vector indices, see this question.
I am now running into a problem of simplification when using the expression as opposed ...
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How can I speed up symbolic integration of this highly oscillatory function?
I am trying to figure out how to speed up this symbolic integration. I have tried parallelization and numerical integration (both I am failing to implement).
Here is the function:
...
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Poincaré half plane model gives all imaginary sides and angles
I want to compute right triangle sides/angles from Poincaré half-plane model in hyperbolic geometry (semi-circle diameters on x-axis ).
$$ \cosh a =\frac{\cos \alpha+\cos \beta}{\sin \beta \sin \gamma}...
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How do I display my output as a complex number with decimals for the real and imaginary components? [closed]
This is my code:
c=Integrate[t/(E^t-1),{t,-Pi,Pi}]/(2Pi) a[j_]:=Integrate[t*Cos[j*t]/(E^t-1),{t,-Pi,Pi}]...
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Series does not deal with the branch cut for the power function correctly [bug]
This is an issue I am having in Mathematica version 13.1.0.0. According to https://functions.wolfram.com/ElementaryFunctions/Power/04/05/02/, the power function should have a branch cut for $x<0$ ...
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Simplifing equation with complex coefficients
I'm trying to simplify an expression with complex coefficients. It should be very straightforward, but for some reason, I cannot get the correct answer. Please, see the code below:
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3
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How to fix this "wrong" analytical integral evaluation?
Integrate[(1/Sqrt[(x + 1)^2 + 1])*(1/Sqrt[1 + x^2]), {x, 0, 1}]
yields
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I want to plot the group delay of the following mathematica code but it takes too long time
I am working on a Mathematica project where I want to plot the group delay. The problem is this code is running too slow. Is there any possibility of speeding up the code?
Here is the original code:
<...
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How can I find a condition for convergence of an integral? [closed]
Wolfram|Alpha says that
$$ \int_0^\infty \frac{x^n}{(x-1)(x-2)} dx=\pi (1-2^n)(\cot(\pi n)+i)$$
for $\text{Re}(n)>-1$. However, for $n=0$, it says the integral doesn't converge, even though it has ...
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Contour integration over lower half of complex plane
I need to perform this integration as a contour integral over the lower half of the complex omega plane with Mathematica.
$$\int_{-\infty }^{\infty } \frac{e^{-i \left(\omega -\omega _0\right) (t-\tau ...
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Why doesn't Conjugate[] conjugate exponentials inside other functions?
Why does something like Conjugate[Sqrt[Exp[I x]]] give output Conjugate[Sqrt[E^(I x)]] instead of ...
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Confused about the output of `CosIntegral`
I am interested in the properties of the cosine integral function, in this case the anti-derivative of Cos[Pi*x]/x, which Mathematica evaluates to ...
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Trying to extract the real part of a real big and may complex number
I have this order 7 polynomium:
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Construct plot of $exp(1/z)$ [closed]
I want to plot the function $f(z) = e^\frac{1}{z}$ in 3 forms:
First to be a plot like [this][1]. But I want to show legend of both magnitude and imaginary part scales.
Second to be a plot only with $\...
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Bugs with `Integrate` when dealing with complex situation?
I'm trying to calculate $\int_0^{\infty } \exp \left(t \left(-x^3+(1+i) x\right)\right) dx$ with mathematica, and different assumptions on t give different results:
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AbsArgPlot for List (Parallel Computation)
Basically, I have a very complicated function that I'd like to draw using AbsArgPlot. I thought it could speed up if I first use ...
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Eliminating complex numbers from solutions
In Maple
eq:=ln(y)-1/2*ln(1+y^2) = x-c1;
solve(eq,y)
In Mathematica
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Series expansion of a given function
I attempt to do the series expansion for the following function
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Why does RegionPlot handle Euler's identity differently for functions and direct expressions?
Edit
When I change the x range (e.g. {x,1,3}) I get the same error also for the direct expression. Thus, the problem exists either way and I assume it just evaluated different points?
Problem
I want ...
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How to generate lattice by integrating over curves on a modular form domain plot?
I was watching this video (2:30 of https://youtu.be/zLEyIT_BCgk?si=ji5NyjR7vcwzaNxi ).
Here in the video he said that to get the lattice , we just integrate over the curve(silver line) and we will ...
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Integrate gives inconsistent result for gamma-like integral with complex variables
I am trying to come up with a generic formula for the below integral, which is analogous to the upper incomplete gamma function,
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Drawing cycles around and across cuts
I want to draw cycles (or paths) around and across the cuts on the complex plane for the following function (where I have put the cuts between [z1,z2] and ...
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How can I find minimal modulus of $z^2 - w z - 4$?
Let $z$ and $w$ be two complex numbers satisfying conditions:
$|z| = 2$ and $|w i - 2 + 5i| = 1.$ How can I find the minimum of $|z^2 - w z - 4|$?
I tried with setting $z = a + b i$ and $w = x + y i$:
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Mathematica crashes when trying to use NIntegrate on a complex function
I am trying to integrate the real part of a specific entry in a Green function given by
G[E_] := Re[Inverse[E iF - H + I L/2]][[13, 13]];
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Contour integral with radius infinite [closed]
How can I get compute a contour integral of the function $f(z)=\exp(i z)/z$ in the upper circle with center in $(0,0)$ and radius $R$? I want verify that $\lim_{R\to \infty}\int_C f(x)=0$ in ...
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Is it possible to express $\text{Li}_2(-\frac18(-i+\sqrt{15})+\text{Li}_2(\frac18 (i+\sqrt{15})$ as an explicit real expression (not numeric)? [closed]
I obtain this expression in my calculations, and numerically I am sure that it is a real number.
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How can I ask Mathematica to give the explicit real form of the given function?
In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, ...
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ParametricNDSolveValue, NMaximize: Dealing with complex results in maximization problem
I analyze a system of differential equations in several variables including mus[t], mui[t], and w[t]. Time runs from t=0 to t=T. The two initial values mus[0] and mui[0] can freely be chosen; their ...
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How to check if there exist variables for which a function may be real?
I have a tough time in checking whether there exist any values of x and y (both real) for which the following pair of functions ...
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MatrixExp sometimes erroneously assumes variables are real
Consider the simple expression
MatrixExp[I Conjugate[x] {{1,0},{0,1}}]
which Mathematica correctly evaluates to
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What to do when FullSimplify runs out of memory?
So close yet so far! I've read a number of posts here about tips and strategies for simplifying expressions. I hope this case still offers guidance to others.
I have an expression that (just!) fits ...
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Basins of attraction using Newton-Raphson method for nonlinear system
I am trying to construct basins of attraction using the newton's method for the system of two equations whose roots are real. I need to develop a code to get basin of attraction. Unfortunately, my ...
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Plot freezes with arbitrary precision complex evaluations
I find that Plot has some strange behavior.
a = {{-5.355`3 I, 0.1589`3 }, {2.305`3, 0.01425`3}};
Det[a] // Abs
gives ...
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ExpToTrig conversion problem
Let we have some ODE solution:
formExp = c1 E^(-I t) + c2 E^(I t) +c3 E^(-2 I t) + c4 E^(2 I t)
It is known that this solution can be reduced to the form:
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Conformal Mapping Function and Scaling Factor
I am having problems determining a scaling factor for a conformal mapping function.
The plan is to map the upper half plane into a rectangle (Schwarz Christoffel Transformation) to determine the ...
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Initial conditions making trouble with NDSolve
I want to solve a number of differential equations in a single NDSolve. The code is as follows:
...
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How can I improve the accuracy of FindRoot for a complex equation?
I want to solve the following problem: Given a complex matrix $m=\textbf{m}(λ, ω)$, with $λ, ω \in \mathbb R$, find $λ$ and $ω$ such that
$$\det[\textbf{m} (λ, ω)] = 0$$
Since one can take the real ...
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Unable to simplify complex expression [closed]
I am very new to Mathematica. Somehow Mathematica doesn't give me the norm expression, instead, it just gives the original expression. How should I fix this? The code is:
...
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Find the Intersection Point of Two Complex Functions Using Complex3DPlot
I want to find the intersection point using ComplexPlot3D. I have a function call it $f(\lambda,k)$ ($k$ is fixed) such that at two particular values of $\lambda_{1,...
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How does mathematica handle roots of complex numbers
When Mathematica takes $(-1)^{\frac{3}{4}}$, is it really interpreting it as $((-1)^3)^{\frac{1}{4}}$, or $((-1)^{\frac{1}{4}})^3$?
These seem like they would give $e^{i \frac{3\pi}{4}}$ versus $\...
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Sqrt returns complex values
I am trying to find sine from a cosine relation using the following commands:
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Differential complex equations in cosmological problem
I want to solve a differential equation of second order with complex initial conditions. Despite I have wrote all the code with detail, I am still facing some problems I might want to review here. The ...
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How to verify that a certain point is a branch point for a complex function using Mathematica?
It is straightforward to verify that z=0 is a branch point for w[z]=Sqrt[z]:
...
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Scope of Simplifying Complex Expressions [duplicate]
Do you know what the scope of Mathematica's simplification capabilities for complex expressions is? For example, I put the heavy lifting of proving a complex inequality on Mathematica, using the ...
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Vector in the complex plane
Please tell me how I can make an animation with rotating vectors rather than rotating points.
...
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How to numerically find complex non-real roots of a function?
Using Mathematica, how can we numerically find only complexes, but not real roots, of a function?
For example, if we have f:C->C, and we have roots like, R1,R2,...,Rn (real roots, without imaginary ...
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Make a "formula-millipede" move along arbitrary path
Math artist Chirag Dudhat specializes in simple math that does something interesting visually. He recently had a hit with a "millipede" simulation with simple complex plane formulas. Below ...
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What is resistivity function of a 3-bar electric switch?
I answered a question on Physics StackExchange - considered as homework - numerically. The question is: What is the resistance of three stacked identical blocks, the middle bar shifted by its half ...
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