# 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.

449 views

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

I have a model called qobs: ...
322 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. ...
111 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 ...
251 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: ...
498 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?
208 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: ...
217 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 ...
441 views

450 views

### Taking real and imaginary parts of indexed functions and speeding up ComplexExpand

I am setting up a large system of ODEs and in order to use the IDA method (which is sig. faster for my system and thus attractive), I must split my equations into real and imaginary parts. I am ...
265 views

### Plot complex path (essentially a 2D path) expressed in one real parameter

Consider a complex path expressed in one real parameter, such as $$f(\alpha)=\frac{1}{e^{i \alpha} + 1},$$ which is a Möbius transformation of the unit circle. I know I can expand it all out and use ...
3k views

### How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
3k views

### How do I find line integrals?

For example, how can I calculate $$\int_{\left | z \right |=1}\frac{dz}{z}$$ I know that the answer is $2\pi i$ but how do I do it using Mathematica?
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### Plotting region $f(S)$ for given complex function $f$ and $S \subseteq \mathbb{C}$ [duplicate]

I have a function $f: \mathbb{C} \rightarrow \mathbb{C}$ and I want to be able to see the effect of $f$ on any particular region of $\mathbb{C}$ e.g. what happens to the unit disk under this ...
608 views

### About Argument of complex numbers

Suppose my z = x + iy Now, if y=0, then z = x i.e it becomes a real number So, logically ...
604 views

### Draw the image of a complex region

I'm working on a complex question that asks that I determine a function that maps the complement of the region $D=\{z:|z+1|\le 1\}\cup\{z: |z-1|\le 1\}$ onto the upper half plane. That is, $f$ must ...
335 views

### Riemann-Spherical Projection of Network onto the $\mathbb{R}^2$-Plane

I'm trying to find a way to plot the graph ...
1k views

### Contour plot of complex function: problem in choosing argument

I have a complex function F[x,y], and now I want to plot the contour F[x,y] = 0. What can I do in order to have the contour plot vs Re[x] and y (That is, I want to treat y a real variable and x a ...
666 views

### How to export a table of complex numbers?

I'm having problems exporting a table of complex numbers. I have: ...
180 views

### A question about derivatives (cubics)

Given an equation: f(z) = a (x + I y)^3 + b (x + I y)^2 + c (x + i y) + d Which can be re-written as: ...
How can I plot the hyperbola represented by the following complex equation: $$\left|z-a\right|-\left|z-b\right|=2t\tag{1}$$ Should I convert (1) into the following form? ...
### Optimization for inequalities in $\mathbb{C}$
I want to check when the expression $$\sqrt{\sqrt{\lambda^{2}\left(2E+\lambda^{2}\right)}+E+\lambda^{2}}$$ is real, when it is purely imaginary and when it is complex (with imaginary part not ...