# 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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### Simultaneous plotting

For my experiment, I have to simultaneously fit the real part and imaginary part of cavity reflection data which is given here column 1: frequency, column 2: reflection magnitude, column 3: phase I ...
153 views

### Conjugate[a/b + c/d]

Trying to obtain the result of Conjugate[a/b+c/d] only gives the same result. As such, I use Refine as: ...
67 views

### Evaluating Bessel-Schläfli-type Integral with Infinite contour

I am attempting to evaluate the integral $$\int_{\infty-i\pi}^{\infty+i\pi} dt \frac{e^{-\frac{l}{n}t}}{[(X'-X)^2+r^2+s^2- 2rs \cosh(t)]},$$ the only variable being $t$, ...
226 views

### Simplifying square root of exponential

Very simple question: Why doesn't Mathematica simplify this square root expression? Refine[Sqrt[Exp[I p]], p > 0] // FullSimplify It should give ...
52 views

### Dynamic input for Complex, Determinant output problems [duplicate]

I'm having trouble using Complex with Dynamic real and imaginary inputs. The inputs come from a matrix of popup menus: ...
128 views

### NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
246 views

### Reduce a complex inequality

Reduce[Abs[1/(1 + I/Sqrt[α])] < 0.5, {α}] It is taking long time to run. Can any one help me to get the reduced condition in terms of $\alpha$ or its modulus. ...
144 views

### Problem of calculating the residue of a expression (to confirm the result from a paper) [duplicate]

I use Mathematica to confirm a result from a paper which is to calculate the residue of a expression at zero. The code and result are given below. Is this residue too complicated for Matheamtia or ...
125 views

### Residue failed to reproduce this residue in a paper

This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ...
107 views

### Factor out imaginary unit of root of obviously negative term

Suppose I have the term $t=\sqrt{-a^2-b^2}$, where $a,b\in\mathbb R$. Of course, we know that it holds $$t = \mathbb i \sqrt{a^2+b^2}$$ which is (in my opinion) more convenient. How can I get ...
84 views

### A simplification of a complex expression

I use mathematica to confirm a result from a paper ("...
37 views

### Compiling LinearSolve with 2 complex matrices, possible bug

Take two complex matrices depending on one variable, for example: ...
78 views

### Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
115 views

### How to calculate this complex expression?

I have a complex expression as follows, ...
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Define: ...
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### Using Arnoldi Method with Multiple Options

I have a matrix with many complex eigenvalues, but I only need a few near a particular complex number. I am only looking at the imaginary parts, so I need the few closest on the imaginary scale to my ...
94 views

### How is it possible that PolyLog[2,1.1] returns an imaginary number?

Given that: PolyLog is defined as li[n_, z_] := Sum[z^k/k^n, {k, 1, ∞}], ...
62 views

### Why can't Mathematica solve this complex equation?

So I want to find the complex part of Rthev,equate it to zero and solve for ω but it won't let me. Is it because it thinks ...
14 views

### Find a conformal map from disc onto trapezoidal plate [migrated]

how can conformal mapping a disk into a trapezoidal plate with defining favorite central point?
155 views

### Integrate and NIntegrate disagreeing over branch cut of Sqrt?

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. In Mathematica 10.2 I'm trying to integrate this piecewise continuous function, but ...
85 views

### Complex Plot with Imaginary Part encoded in color

Heyhey, I wanted to plot the complex cosine in a 3D graphic where the real part is given by the surface, while the imaginary part shall be indicated by the color. Therefor, I tried the code ...
79 views

### Plotting the modular surface of a complex function [closed]

Tristan Needham stated in the introduction to Visual Complex Analysis that he used Mathematica to create the majority of graphs in his book. I'm trying to recreate the graph he made for figure[14] of ...
139 views

### Symbolic and numeric limit disagreeing on branch cut of ArcTan

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. Investigating comments to my previous question lead me to the following problem: ...
101 views

### Integral over real valued function becomes complex

I've tried to solve the following integral, but I get a complex solution even tough it should only have a real part. $$f(x)=- \frac{10^{-20} x}{0.99005- e^{10^{-12}x}}$$ Now I want to calculate the ...
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### How to find the pole of a equation where the residue exist？

I want to calculate the residue of an equation, such as: equ = 1/((x - 2)Sqrt[x - 1]) So first I need to find the pole of the equation. My method is find the ...
80 views

### Write complex number in terms of absolute value and phase

I have a long vector and some of the values (19 out of 64) are complex. I got them using the Mathematica Rationalize function, so the complex ones are written in the a+bi form. Is there a function I ...
71 views

### Generating OpenCL C code [closed]

I'm trying to make an interactive complex function plotter using OpenCl. So far I can only plot functions that I hardcode into the kernel by hand. I'd like to be able to use ...
34 views

### Performance of Apart with complex numbers

Consider the following code ...
49 views

### Finding Complex expression [closed]

How do you find a real part of a complex expression? Here is an example of what I am looking for complexExpand[Sqrt[x + I*b]] gives me ...
109 views

### Calling Integrate with many limits of integration

I accidentally discovered that you can put many numbers into the limits of integration of Integrate and Mathematica will still evaluate it without returning an ...