# 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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### Translating syntax of a pure function

I have a matrix in complex exponential form. I want to factor out the complex exponential form and then express the inside in the a+i*b form. For example: \begin{bmatrix} e^{i \frac{\pi}{4}} ...
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### What is the reason that $zz^*$ is not written as $|z|^2$ sometimes?

For a general (complex) number $z$ I sometimes get terms that explicitly writes (for instance) $$2zz^*+|z|^2.$$ I should add that these expressions come from long calculations involving packages ...
177 views

### Complex result for Real vectors in VectorAngle

I was expecting a real angle using VectorAngle when passing real valued vectors, but I obtained a complex angle: ...
44 views

### Theory Of Improper Integrals and its Application [closed]

am writing a project on the above topic, I can do with a lil help Plsss, thank u very much, basically am supposed to do a paper on it, like it's a topic under complex analysis and I have been reading ...
134 views

### Why does Mathematica give this ArcSin[2] result?

The code N[ArcSin[2]] evaluates to 1.5708 − 1.31696 I but it should be undefined instead because it is on the branch ...
371 views

### Compiling the VoigtDistribution PDF

According to List of compilable functions, Erf and Erfc are compilable functions. However, I want to make a compiled version ...
118 views

### Non-algebraic equation in the set of complex numbers

The following equation in $\mathbb{C}$: $4z^2+8|z|^2-3=0$ is not algebraic and has 4 solutions : $\pm\frac{1}{2}$ and $\pm i\frac{\sqrt{3}}{2}$. The Solve function in Mathematica only returns the 2 ...
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### How to instruct mathematica that $\delta^*$ is the conjugate of $\delta$

I have this code: ...
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### Finding extremums of Abs[complex function]

We have a function same as f[x_]=Cos[x] Cos[2 x] + I Sin[x] Sin[2 x] The final objective is to find all extremums of Abs[f[x]] in [0,2 pi]. But in the first ...
83 views

### Simplifying complex fractions

How can I simplify a complex fraction in order to get something of the shape (a + I b)/(c + I d)? Note that I would not like Mathematica to further simplify it ...
245 views

### Plot Two Circles and color their difference

I am trying to plot two circles with radius 1 and another with radius 9. Both are centered at $(0,-1)$. I then want to color in the distance between the circle of radius 9 and the circle of radius 1. ...
272 views

### Defining a General Complex Number

I am trying to compute the Complex conjugate of two complex numbers multiplied together. However, when I go to define my complex numbers as $a+b I$ and $c+dI$ it does not like $b$ and $d$ because they ...
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### Solve for when two symbolic complex numbers are equal

I'd like Mathematica to to show that two complex numbers $a + b i$ and $c + d i$ (with real coefficients $a, b, c, d$) are equal if and only if $a = c$ and $b = d$. The obvious thing does not quite ...
158 views

### How to test if elements of an array are real or complex?

I am new to Mathematica and I have to select the elements in an array that only contain real numbers and eliminate the ones that have complex parts. Basically the code that I have is an array of ...
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### My evaluation is taking a lot of time

I was evaluating the roots of a transcendental equation, when I noticed that Mathematica never finishes but stays in the running state. The following is the code that I was using: ...
881 views

### Complex conjugate

How do I complex conjugate a vector? ...
744 views

### Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitly. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
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I evaluated ...
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### How to solve coupled complex-valued equations faster and get simplified solution

I have six coupled equations. How to solve these equations symbolically faster in Mathematica. In these equations, variables p,q,x,y are ...
42 views

### Solving a differential equation with a complex (independent) varible

I'm trying to plug in complex values in the numerical solutions of ODEs without success. For instance y[I] /. NDSolve[{y'[x] == 0, y[0] == 3}, y, {x, -10, 10}] ...
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### Returning all branches of a multiple-valued function

This question and answer was inspired by this closed as duplicate question. One possible definition of the n-th order root of x ...
Can someone share how to find a Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at zero on the annular disk $1<|z|<2$?