# 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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### Conjugate of I \[Phi] [closed]

I have a bigger expression of which I have to take the conjugate. But this is in itself perplexing. When I write ComplexExpand[Conjugate[I\[Phi]]] I just get ...
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1k views

### Complex conjugate

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

### Working with derivative of conjugate of a complex number

I have a complex function, lets say $g(x)$. I want to take its and its conjugate's derivative. I need the solution of derivative which must be symbolically and computationally efficient. Lets take an ...
77 views

### Factor bivariate polynomial over the complex numbers

This is very much like Factoring polynomials to factors involving complex coefficients except that I'm concerned about bivariate polynomials, not univariate polynomials. Take for example the ...
591 views

### How to calculate the phase spectrum

I have the following frequency characteristics in the Fourier domain: $$H(\omega)=\frac{-\omega^2}{63170s^{-2}-\omega^2+355.1s^{-1}i\omega}$$ How do I find the phase spectrum from this? I should ...
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### For the same function, why does /. give a complex result?

I define a very simple function like this, g[k_] := 1. + 2 Sum[1/(1 + (2 n)^2), {n, 1, k}] g[50] give the result is: 1.70279. But g[n] /. n -> 50 give aother result: ...
115 views

### Optimizing complex functions

I am trying to optimize a function containing complex numbers, however I keep running into errors. Consider the simple optimization problem: ...
197 views

### How to obtain Laurent series coefficients of an (almost) arbitrary function?

I have observed that Series in Mathematica assumes that the given function is smooth in the point around which one wants to perform series expansion. For instance: ...
131 views

### Pattern matching with Complex. Feature or a bug?

fixed in 10.1 (windows) I have run into some strange behavior while doing some pattern matching. First, this works as expected: ...
167 views

### Plotting Complex Numbers - Functions of Complex Numbers [duplicate]

So I have to generate a few different plots with z, where z is a complete number... z[x_, y_] := x + y*I F[z_] := (25*Pi*z*I)/(1 + 10*Pi*z*I) First, I need to ...
189 views

### Complex number plot with inequalities [duplicate]

I need to plot the function where z is a complex number: $$S = {z:|z + 0.15|<0.6} \wedge {z:Pi/4<=arg(z)<=Pi}$$ I can do this: ...
279 views

### Differentiation of an unknown function

I have to take the partial differentiation of an unknown function. For example, take the unknown function to be $g(x)$. Then it's derivative w.r.t $x$ is $g'(x)$. By default, Mathematica ...
197 views

### Trying to get Arg[1 + I a] -> ArcTan[a]

Can Mathematica evaluate Arg[1+ I a] when a is a positive real in order to get ArcTan[a]? ...
247 views

### Singularity on a simple Plot

While solving quartic equation ...
86 views

### Evaluating an integral

Here is the input: Integrate[E^(2 I*t)/(2*Pi*(E^(I*t) - z)), {t, 0, 2 Pi}] and here the output: ...
241 views

### NIntegrate and Integrate giving different results for ill-behaved function

I'm trying to integrate the following function with Mathematica 8: $$I(a,b)= \int_0^1 \mathrm{d}x\int_0^1\mathrm{d}y \,\theta(1-x-y) \frac{1}{x a^2-y(1-y)b^2},$$ where $\theta$ is the Heaviside ...
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### How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
531 views

### $L = \lim\limits_{z \to 1} \frac{1-z}{1-z^\ast}$ evaluates incorrectly

I'm about 90% certain this is a Mathematica issue, not me making a silly mistake. I'm trying to evaluate $$L = \lim_{z \to 1} \frac{1-z}{1-z^\ast}.$$ Naively entering ...
65 views

### Why is PolyLog[] giving weird answers for ordinary values? [duplicate]

Possibly related to this question, but it seems slightly different: Strange behaviour of PolyLog Function Wikipedia says that for real s, z<1 should be real. So I was confused when MMa returned: ...
72 views

### Plot of the set complex numbers [duplicate]

I want to show this set (eigenvalues of my matrix): ...
57 views

### Complex input for Compile makes it slow

I asked a question here and then tried to use Compile for the solution to gain even more speed. Inside Compile there is a loop ...
186 views

### Complex Integration

There are some sequential functions: ...
176 views

### Matrix form of complex numbers [closed]

Complex numbers have matrix form. But some 2x2 matrices while differ, represent the same complex number. To compare complex numbers one has to transform the matrices to the form \begin{pmatrix} a &...
314 views

### Evaluating the real part of an expression

I want to get the Real part of this expression - shouldn't be too hard to evaluate. Why is Mathematica not evaluating but returning the same code? ...
9k views

### How to tell Mathematica that certain variables are real/imaginary, integer-valued, etc

I'm trying to expedite some quantum mechanical calculations by running them through Mathematica. Expectation values and stuff like that. When I say, for example, ...
169 views

### 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 ...
454 views

### 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. ...
394 views

### 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
244 views

### 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 ...
190 views

### 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 ...
751 views

### 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 $v=2xy$, ...
2k views

### Möbius transformations revealed

Möbius Transformations Revealed is a short video that vividly illustrates the simplicity of Möbius transformations when viewed as rigid motions of the Riemann sphere. It was one of the winners in the ...
403 views

### 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 ...
384 views

### Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form \left\{ \begin{align} i\frac{da_1}{dt} &=...
446 views

### Listplot imaginary part of complex numbers

I have the following list w={{0.01,99 +0.00001414 I},{0.15,6.6370108 +0.003144129 I},{0.25,3.9515722 +0.00854493297 I},{6,0.10041 +0.28132187 I}} and I want to <...
446 views

### Speed up Schwarz-Christoffel mapping

I would like to ask your advice how to speed up Contour and Parametric plots in the following example. Let as start by defining a function ...
241 views

### Why does N[Re@f] give complex result?

Consider this code: ...
172 views

### Optimizing a function containing a complex exponential

I've noticed the following significant different in performance for different formulations of the same function: ...
Why can't Mathematica solve $\quad\quad\frac{1-i}{\sqrt{2}}=e^{i \alpha } \tan \left(\frac{\beta }{2}\right)$ with the restrictions $\alpha \in [0, 2 \, \pi)$ and $\beta \in [0,\pi]$: ...