# 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 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: ...
145 views

### 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 $$A=\{z\in \mathbb{C},z+e^{z}=0\},\\A=\{z\in \mathbb{C},\Re(z)+e^{z}\geq0\}.$$
325 views

### 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 ...
218 views

### 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 ...
129 views

### 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 ...
355 views

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### About how Mathematica understands the branchcuts of the complex logarithm [Part 3] [closed]

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 ...
60 views

### Conjugate of InterpolatingFunction?

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

### Getting Arg[z] to go from $0$ to $2\pi$

I'm defining branch cut functions, and I'm using $\arg(z)$ as a building block. So I just spent an hour at the whiteboard assuming that $\arg(z)$ goes from $0$ to $2\pi$, and then I implement the code,...
54 views

### Always the same problem with Conjugate [duplicate]

I want to compute something like : ...
2k views

### How does Mathematica understand branchcuts of the complex logarithm?

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 ...
510 views

### FindFit::nrlnum What am I doing wrong?

I have a model called qobs: ...
338 views

### Series expansion of a complex function

How do I expand a function $f(z)$ in a particular region? For example, how would I expand $f(z)=(z^2-3z+2)^{-1}$ in the region $0<|z-1|<1.$? I believe this can be done by the binomial theorem. ...
112 views

### How to apply RootLocusPlot correctly

I have to analyze the complex regions of variable c which is define obtained with InverseLaplace help in the form ...
273 views

### Determine types of input, output and internal variables in compiled functions

I am trying to speedup the computation of a longer function using Compile. For illustration consider the following short example: ...
538 views

### How to apply a conformal map to a jpg (or other image) [duplicate]

I would like to apply a conformal map to a jpg. For example, the map $z\mapsto z^2$ to this image: http://thumbs3.ebaystatic.com/d/l225/m/mGyeriV7l-YArkeBd9oMUng.jpg Any help on how to do this?
227 views

### Simplifying complex expressions

I'm trying to work with complexes and I want Mathematica to know that all variables are real unless I explicitly assigned the variable with an I so I wrote: ...
227 views

### How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be <...
472 views

### How to find the complex number has least and greatest modul satisfying a given condition?

Let be given the complex number $z$ satisfying the condition $|z-2+2i|=2\sqrt{2}$. I want to find the complex numbers $z$ so that their modul obtain least and greatest value. I tried. Put $z = x + y i$...
113 views

Going through Derbyshire's Prime Obsession & trying to take LogIntegral of 20^ZetaZero[1] & comes up with a value of <...
36 views

### Check if a (possibly nested) list is real [duplicate]

I have a very large matrix of numbers. I want to check if all its entries are real. At the moment I am using realQ = And @@ Thread[Flatten[Im @ #] == 0] & Is ...
1k views

### How to get rid of all complex numbers and functions?

For almost esthetical reasons, I always have been fascinated by infinite sums of series and I always wonder if theyhave a closed form. A couple of days ago, I found on MSE a question related to the ...
276 views

### How to compute the residue of $e^{z-\frac{1}{z}}$ at z=0?

I've tried the following but it didn't work: Residue[Exp[z - 1/z], {z, 0}] not even this: Residue[Exp[1/z], {z, 0}] ...
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360 views

### Plotting discrete points on a phase plot

I'm trying to generate a phase plot of a sinusoidal voltage at discrete points using the following code: ...
138 views

### Need to take infinite sum of residues, is there a way to choose the order of operations for ReleaseHold?

I'm computing an infinite sum of residues. I want to do something like this: ...
268 views

### Decomposing a complex numbers equation into its real and imaginary part

I have an equation such as: a*z^2 + b*(z - c)^2 == d where z is a complex variable and a,...
259 views

### Complex limit gives wrong answer

I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...
5k views

### Simple way to plot a complex valued function of one real variable

How can I plot a complex valued function of one real variable, $f(t)$, as $$x=-\Re f(t),\ z=\Im\ f(t),\ y=t \space?$$ My aim is a 3-dimensional path, treating the complex valued function as if it ...
I want to solve the equation $\frac{abi}{a+bi}=4-2i$, where $a$ and $b$ are real numbers. I know from hand-solving the answer is $a=5$, $b=-10$. How do I get Mathematica to tell me this? I tried: <...