# 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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### Expansion for Modified Bessel Function Around Infinity

I'm somewhat new to Mathematica, and I don't understand why I'm getting inconsistent series expansions for the modified Bessel Function of first kind near $x=\infty$. First problem: I get different ...
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### Plot[Im[f[x]],…] incorrectly gives graph of identical zero function

Consider Plot[Im[(1 + (-1)^(2/3)*x)/((-1)^(2/3) + x)], {x, 0, 1}] At least in Mma 11 it gives the following picture: Meanwhile, ...
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### Linearity of the Conjugate operator

The output of Grad[Conjugate[x + y + z], {x, y, z}] is ...
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### How MandelbrotSetBoettcher function is computed?

Boettcher function is a solution of Boettcher's functional equation, so in case of complex quadratic map: $B(f(z)) = (B(z))^2$ where: B is Boettchers function f is complex quadratic map There is a ...
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### FunctionDomain working with real part

Is there any reason why Mathematica evaluates the following FunctionDomain[Re[((I + 1) x)], x] (* False *) as False, where I'...
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### Amplitude of a transfer function

I'm looking to calculate the amplitude of a transfer function which is defined in a symbolic way : T=(1 + 2 I r λ)/(1 - r^2 + 2 I r λ) I try this, i doesn't work ...
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### Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
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### The number of real values assumed by combinations of complex roots of a decic

Define complex conjugate as the pair of complex numbers $a+bi,a-bi$. Assume you have 5 such pairs and they are the 10 roots $x_i$ of a 10th-deg equation with integer coefficients. In general, how many ...
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### Simple contour integral with a parameter gone wrong

Bug introduced in 7.0 and fixed in 7.0.1 I run into the following problem, I tried to evaluate a very simple integral: ...
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### Specifying Contours in “CyclicReImLogAbs” for ComplexPlot/ComplexPlot3D

How can I specify where and/or how many contours appear in ComplexPlot and ComplexPlot3D when using the "CyclicReImLogAbs" color function? I'm referring specifically to the black and white ...
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### Integrating real function gives a complex value

I want to integrate this quite complicated function Sin[2 Pi n x r0/L]*u[x, (m + 1/2) Pi - (nu I Pi/2), kappa I, nu] over x, where ...
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### How to write a complex no linear term in loop of a differential equation system?

I have this system of equations $$i \frac{d \psi_{m}}{dt} = k \psi_{m-1} + k \psi_{m+1} + \gamma \vert \psi_{m} \vert^{2} \psi_{m}$$ and this is my code ...
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### numerical integration of an integral with singularity

I want to compute the following integral numerically in Mathematica, $$\int_{-\infty}^{\infty} dw' \;\frac{\Gamma(\delta-4iw') 4^{4iw'}}{(i(w'-1)+\epsilon)^{1-4iw'}}$$ where $0<\epsilon, \delta≪1$...
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### One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
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### Integrate returning complex values

I am having trouble using mathematica to calculate some integrals Namely this : ...
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### How do you define the domain and range of the variables for a plot?

How do I define the domain to be only reals and the range to be only complexes? Everytime I plot using ComplexPlot[], I get a C->C function so there are basically too many variables to plot and I ...
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### Ordinary differential equation in the real domain

If I have the following equation (y - 1) ^5 == 32 I can select the real solution with Solve[(y - 1) ^5 == 32, x, Reals] Now, I ...
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### What are “VariableReplacementDump” and “TranscendentalDump”?

I have run into a Mathematica object I've never seen before and Googling those reveals nothing. I'm talking about VariableReplacementDump and ...
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### Simplification of expression with sum of absolute values

I try to simplify following expression 1/2*(Abs[a1] + Abs[b1] + Abs[c1] + Abs[d1]), where a1, b1, c1, d1 are quite long: ...
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### Change the PolyLog branch cut in Wolfram Mathematica

The problem is to change the branch cut of PolyLog[2,z] function from the default half line z=1+x, x>0 to the new one ...
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### Mathematica cannot evaluate the real part of a fraction?

I am encountering some confusing behaviour with Mathematica that maybe you can help me resolve: If I type: Im[1/a]~Refine~(a \[Element] Reals) I get the output: ...
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### Solving ODEs in the Complex Plane for General z

I saw with the new 12.0 update, they have introduced expanded functionality for solving complex ODEs. In the given example, they solve for $y(t)$ and plot results using the new ...