# Tagged Questions

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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### How do I declare that a variable represents a real number?

How do I tell Mathematica that a variable is a real number. I searched for this question here and in Google and nothing that was suggested seems to work for me. I must be missing something. My code is ...
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### Problem on limit involving complex numbers

I have $${\frac{(6 k+1)^{k}}{(2 k+5)^{k}}}*(z-2 i)^k$$ and I need to find it's limit for $k$ approaching infinity. ...
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### Why is it so complicated to simplify a complex conjugate? [closed]

My question is very simple. I would like to multiply a complex number by its conjugate. Unfortunately, this seems to be extremely complicated in Mathematica. Consider the very basic example: ...
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### Simplification of a complex-valued expression with purely real components

(I'm including all the information here, as I'm not sure how much of it is necessary to solve the problem. For a tl;dr skip to the bottom) I've been working on a problem involving calculating ...
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### How find solve the equation complex conjugate? [closed]

Tried solving it with every function I know but couldn't z*=z^2
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### How to find all roots of a complex number [duplicate]

Finding all roots, and I know there are four f them, of this (1 - i)^(1/4) Not only real, but imaginary as well
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### Rationalize complex numbers

What is the best way to rationalize complex numbers, if not both the real and imaginary part are actually rational? According to the documentation, Rationalize ...
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### Plot Complex Function [duplicate]

I want to have a 3D plot for the following function: (1.6 - 0.005 I) E^(-0.5 p^2 + ( 2. I) p q + (6.5 - 11 q) q) p and q from -10 to 10 Is there any way?
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### A question about expanding complex functions of real arguments

I have the following problem. There is such an expression as: P[x_,y_] := z[y] E^(I beta x) + Conjugate[z[y] E^(I beta x)]; The variables ...
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### ComplexExpand does not treat everything as real number

ComplexExpand does not treat everything as real number?? Please read the following simple example ...
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### How do I plot the images of oriented curves under complex transformation?

I'm working on a complex transformation sketch that I'd like to create via mathematica. I'm working with the function $$w=z^2\tag{0},$$ where its real and imaginary parts are $u=x^2-y^2$ and $v=2xy$, ...
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### Mobius transformations revealed

Mobius Transformations Revealed is a short video that vividly illustrates the simplicity of Mobius transformations when viewed as rigid motions of the Riemann sphere. It was one of the winners in the ...
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### Real and Imaginary parts of solutions to a complex linear ODE system

Consider a complex linear ODE system $x'=Ax$, where $$A=\left( \begin{matrix} 0&1\\ -2&-i \end{matrix}\right).$$ One can first find the eigenvalues and eigenvectors using ...
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### How to solve the warning problem and obtain real roots without imaginary part?

I am trying to solve a equation with Newton's method via FindRoot, and the codes are: Define the functions: ...
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### Plot sets in the complex plane [duplicate]

I just want to know if there's a way to plot sets in the complex plane. For example $$A=\{z\in \mathbb{C},z+e^{z}=0\},\\A=\{z\in \mathbb{C},\Re(z)+e^{z}\geq0\}.$$
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### Express a complex function $f(z)$ as $u(x,y)+iv(x,y)$

How can I write a complex function $f(z)$ in the form $u(x,y)+iv(x,y)$ using Mathematica? Re and Im do not work, because they do it for complex numbers, not functions. For example, if I try ...
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### Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
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### How do I solve for the real and complex parts of an equation simultaneously?

If I were to have an equation, say something similar to... (1-Sqrt[x - I y])/(1+Sqrt[x - I y]) = A + I B Where I = Sqrt[-1], is there a way for Mathematica to ...
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### About how Mathematica understands the branchcuts of the complex logarithm [Part 3]

One understands that for the function $\log(z^2+a^2)$ Mathematica implicitly puts the branch cuts to be starting at $\pm ia$ and going up/down respectively on the imaginary axis. The phase of this ...
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### Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
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### Always the same problem with Conjugate [duplicate]

I want to compute something like : ...
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### Fastest way to create a NxNxNxN dimensional matrix

I have a function that outputs a complex number Func[x_,y_]:= blah blah; I have constructed a table of all possible values of this function. ...
Say I have the function $f(x) = x \tanh(\pi x) \log (x^2 +a^2)$ where $a$ is some positive real number. Then it seems to be me that Mathematica when given such a ...