# 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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### 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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### Interval arithmetics and complex numbers

I am trying to do some simple calculations for a computer assisted proof and since they are not too demanding I thought of using Mathematica. I seems that Mathematica is great for interval ...
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### 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 ...
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### Finding consecutive residues of large expression?

I have given a large expression expr (has LeafCount of 2772, you can find it in this file or ...
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### Real part of a sum

I would like to take the real part of the following expression: Sum[(a[i] + I b[i]) r^i/(r^2 + z^2)^i, {i, 0, 2 n}] where all of ...
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### Complex input for Compile makes it slow

I asked a question here and then tried to use Compile for the solution to gain even more speed. Inside Compile there is a loop ...
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### Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form \left\{ \begin{align} i\frac{da_1}{dt} &=...
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### Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...