Questions tagged [complex]

Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.

Filter by
Sorted by
Tagged with
0 votes
0 answers
4 views

ComplexExpand of Hypergeometric function

I would like to take the derivative of the absolute-squared value of a hypergeometric function and plot the result, for real arguments ...
user avatar
  • 265
0 votes
1 answer
12 views

Argument of a complex number with assumptions

I am trying to calculate the argument of a complex number: Arg[Cos[y]*Exp[I x]] where both x and y are real. The solution is clearly x, but I can't get it with ...
user avatar
3 votes
0 answers
122 views

Possible bug in ResidueSum

Trying a new command of version 13.1 ResidueSum, I obtain FunctionMeromorphic[{(x^2 - x + 2)/x, Abs[x] > 5}, x] ...
user avatar
  • 17.2k
0 votes
0 answers
31 views

Modulus square of an complex expression

I have an expression: E^(I*((-k)*x + \[Xi] - (t + 1/2)^y/(\[Beta]*Subscript[b, 2]*(Subscript[a, 2] + 2*k*Subscript[b, 2])))) I want to get modulus square of this ...
user avatar
  • 503
2 votes
3 answers
103 views

Simplification of complex number factors out an extra i

When I evaluate Simplify[ - a - I Sqrt[3] a - b - I Sqrt[3] b ] Mathematica returns -I (-I + Sqrt[3]) (a + b) Personally, I ...
user avatar
  • 950
-1 votes
1 answer
46 views

ComplexExpand over various imaginary parts? [closed]

I have an equation a=(c+ I d); b=(e+ I f); I want to solve dd=(a C0 * b K C0)/(a C0 + b K C0); both e and f are imaginary ...
user avatar
0 votes
0 answers
47 views

Solving a complex value coupled ODEs with NDSolve

I am a very beginner in Mathematica and I am trying to solve a complex value coupled ODEs with NDSolver. The equations would be like 1 where u refers to u(t) and a refers to a(t), other symbols such ...
user avatar
3 votes
1 answer
49 views

How do I get the complex conjugate of my interpolation?

I import an interpolation from C++ into mathematica which I then modify. Is there a way to obtain the conjugate of the interpolation? Or do I need to use $(f g)^* = f^* g^*$ and export the conjugated ...
user avatar
4 votes
2 answers
105 views

ComplexExpand no longer assumes Derivative[__][__][__] as real

Bug introduced after 11.3, in or before 12.3, persisting through 13.0. Consider the following sample: {Re, Im}[u'[t]] // Through // ComplexExpand In v9.0.1 ...
user avatar
  • 52.8k
1 vote
1 answer
41 views

Issue with using complexplot with Nearest

I have been trying to create a certain fractal with Mathematica but the main issue is that if I try and do something like ...
user avatar
1 vote
0 answers
80 views

Solve 2x2 complex unitary matrix with constains using Solve does not work

I have a 2x2 complex-valued matrix, $U=\pmatrix{U_{1,1}e^{i\theta_{1,1}}&U_{1,2}e^{i\theta_{1,2}}\\ U_{2,1}e^{i\theta_{2,1}}&U_{2,2}e^{i\theta_{2,2}}}$ which I must impose two ...
user avatar
1 vote
0 answers
86 views

NDSolve for complex pde

My goal is to use NDSolve to solve the complex pde $F(z,t)$ with complex derivative $\partial_{z}=\frac{1}{2}(\partial_{x}-i \partial_{y}).$ The equation can be ...
user avatar
0 votes
1 answer
45 views

Unable to simplify exponential expression to its simplest form of trigonometric expression by Euler's formula

Applying "FullSimplify" fails to simplify the following expressions: Input: ...
user avatar
  • 3
0 votes
1 answer
65 views

Plotting a long and complex airy function

I try to plot an Airy function ...
user avatar
  • 269
0 votes
0 answers
69 views

Roots of a transcendental equation with unknown a complex number

I am trying to solve a problem and I got stuck with a complicated transcendental equation. I intend to find these roots. Here, $\omega$ is a complex number, whose imaginary part can be positive or ...
user avatar
2 votes
1 answer
41 views

WolframClient output convert to python complex array

I encountered the following issue with WolframClient. I have a my.function file which contains some function that takes some ...
user avatar
  • 513
9 votes
2 answers
152 views

Getting the "correct" branch of a complex function

This stuff always trips me up. I'm trying to plot a function and I think that the plot looks good in one region and isn't really what I'm expecting in another: The right side of the plot is what I am ...
user avatar
  • 1,478
2 votes
0 answers
77 views

Theory behind CountRoots

According to this page, one can compute the number of zeros of a meromorphic function over an interval in Mathematica. I am working with univariate functions of x, which are meromorphic elementary ...
user avatar
4 votes
5 answers
139 views

Display Conjugate[x_] as a long overbar permanently

In TraditionalForm output, I would like to have Conjugate be always displayed as an overbar, not an asterisk superscript. In particular for complicated expressions like ...
user avatar
  • 140
0 votes
0 answers
47 views

Evaluation involving complex conjugates

I was trying to write an expression involving Conjugate. To create a minimal example, however, I have reduced it down to these expressions. ...
user avatar
  • 16.2k
0 votes
0 answers
75 views

Plotting the image of $\Omega=\{z=x+iy \in \Bbb C \mid 1 \le x \le 2, 4\pi \le y \le 7\pi \}$ under $f(z)=e^z$

I'm trying to plot the image of the the set $\Omega=\{z=x+iy \in \Bbb C \mid 1 \le x \le 2, 4\pi \le y \le 7\pi \}$ under $f(z)=e^z$, but I cannot find right function to do this from the docs. Could ...
user avatar
  • 1
1 vote
1 answer
81 views

Divide by zero warning: Actual division by zero or spurious?

I have the following code that calculates the gain of an amplifier ...
user avatar
  • 345
2 votes
1 answer
88 views

Mathematica is messing around with absolute values and sqrts of complex numbers?

I know that $$\begin{pmatrix}0&Z\\Z^*&0\end{pmatrix} \quad\text{has eigenvalues}\quad \lambda_\pm=\pm|Z|$$ but Mathematica gives me ...
user avatar
  • 385
2 votes
1 answer
84 views

How to draw a tangent line for complex function?

I'm new with Mathematica and I have a problem with that, It would be great if you could help me with that. I try to draw a maximum slope of a plot in the same diagram using resource function tangent ...
user avatar
2 votes
1 answer
59 views

Simplifying a power of complex exponential quotient

I have an expression of the form $(\frac{-1+e^{i\,N\,\phi}}{-1+e^{i \phi}})^n$. I want to use mma to hopefully simplify it. I have tried ComplexExpand[], PowerExpand[] with simplifying assumption in ...
user avatar
1 vote
1 answer
60 views

How do I plot different parts of a same function?

Let's say that I got a complex function $f$ of a real variable $x$, i.e. $f(x)$. Suppose that I want to plot the real part of $f$, i.e. $\Re(f(x))$. My question is: should I enclose ...
user avatar
  • 55
-1 votes
1 answer
133 views

Solution this problem to illustrate the conformal mapping [duplicate]

Find the mapping of circle using confirmal mapping ( joukowski tansformation method) Assume w= z+1/z 〖z=re〗^iθ = 〖r(cosθ+isinθ)〗^1 ( a Circle with radius r and center (0,0))
user avatar
  • 7
0 votes
1 answer
69 views

Plotting branch cuts of complex functions

I’m reading the wolfram page on complex functions and noticed that one can actually plot the values of these functions on the axis (cf. image attached). How can I do this in mathematics, say for $sech(...
user avatar
3 votes
1 answer
62 views

How to adapt or mimic the AbsArgPlot default ColorFunction

I like the way AbsArgPlot uses a default ColorFunction that cycles through the hues with much less variation in perceived ...
user avatar
  • 83
1 vote
1 answer
59 views

How to plot "Re-Im" 3d plot with `ComplexPlot3D` (`MeshFunctions -> {Re[#2] &, Im[#2] &}` should work, but doesn't)

By default the f[z_] = ((z^2 - 1)*((z - 2 - I)^2)) / (z^2 + 2 + 2*I) ComplexPlot3D[f[z], {z, 10}] will output AbsArg 3d plot (...
user avatar
  • 123
2 votes
3 answers
307 views

Illustrate the conformal mapping

Find the image of the circle $|z|=1$ by using the transformation $$w=z+2+4i$$
user avatar
  • 49
1 vote
2 answers
105 views

getting rid of complex numbers in a solution list

I have the following list: [0.312712544956844, 0.287641445144978 - 0.306854031390629*I, 0.287641445144978 + 0.306854031390629*I] I would like to get rid of the ...
user avatar
  • 19
0 votes
1 answer
70 views

Spurious poles in a gain plot (due to machine precision or complex numbers?)

I have the following plot that I like to make. It details the gain of an amplifier. ...
user avatar
  • 345
3 votes
4 answers
100 views

How to get mathematica to work out residues of $f(z)=-\left(\frac{z-1}{z+1}\right)^2\frac{2n/z}{z^{2n}-1}$?

Using the function, $f(z)=-\left(\frac{z-1}{z+1}\right)^2\frac{2n/z}{z^{2n}-1}$, should give residues as follows: $ \begin{align} \ &\left(\operatorname*{Res}_{z=0}(f(z))+\operatorname*{Res}_{z=-...
user avatar
  • 325
2 votes
1 answer
75 views

Some help for rewriting this complex function [closed]

I have here a complex function in which z =x+ I y must be filled in f[z_] := E^(-z^2) By hand : ...
user avatar
  • 649
0 votes
3 answers
200 views

A famous Integral from Cauchy deriving, how? [closed]

A example of calculating line integrals in the complex plane Integrate[Cos[2*b*x]/E^x^2, {x, 0, Infinity}] = $\frac{1}{2} \sqrt{\pi } e^{-b^2}$ ( this is the famous ...
user avatar
  • 649
1 vote
2 answers
71 views

Mathematica not assuming real parameters

I have this expression: Eqn = (Cgd rg)/(Cgd+Cgs)+(Cgs rg)/(Cgd+Cgs)-I/(w (Cgd+Cgs)) When I try to evaluate it: ...
user avatar
3 votes
2 answers
170 views

Complex Map Using ComplexRegionPlot

I am self-studying complex analysis using Dennis Zill's, A First Course in Complex Analysis. I'm a bit stuck on one of the exercises in Chapter 2.4, which asks us to find the image of the region shown ...
user avatar
  • 199
2 votes
1 answer
68 views

Simplifying an expression with complex conjugates

I have been unable to do the following. First I make an assumption $Assumptions = x \[Element] Reals; and define ...
user avatar
  • 79
0 votes
0 answers
57 views

Using ColorData to obtain four colors

I would like to reproduce the plot shown in fig(b) from the link. How can I obtain yellow, red, green and blue using the command? Let's say there are 4 roots in total. In this case roots will be {2, ...
user avatar
-1 votes
1 answer
96 views

Please help me insert this example into Mathematica to illustrate the transformation

Please help me insert this example into Mathematica to illustrate the transformation
user avatar
  • 3
2 votes
1 answer
76 views

How to calculate an `InverseMellinTransform` up to its definition in Mathematica?

I have a question about how to calculate Inverse Mellin Transformation's in Mathematica, one way or the other. Look at these findings. The following integral results in Gamma[s]. ...
user avatar
3 votes
1 answer
118 views

FunctionDomain and FindInstance problem

I have some functions including many real parameters as follows: For example, ...
user avatar
2 votes
2 answers
88 views

How do I keep track of the discontinuous jumps of the argument of a complex function along a contour in the complex plane in Mathematica?

In complex analysis, let's say I choose a branch of the complex logarithm (so that I can calculate the argument of a complex function), and I want to study numerically the variation of the argument ...
user avatar
1 vote
2 answers
573 views

Mathematica `fourier` get different result with python `np.fft` [closed]

In python,I run fft as below: ...
user avatar
  • 697
10 votes
1 answer
199 views

NIntegrate can't handle InterpolatingFunction produced by FiniteElement properly?

Bug introduced in 12.3.1 or earlier and fixed in 13.1.0 This is a problem comes out in the discussion here and I think it's worth posting a new question for it. Consider the following sample: ...
user avatar
  • 52.8k
2 votes
1 answer
104 views

Integrate does not converge while Fourier transform does

Let us say I want Mathematica to compute the integral $$\int dx \, \text{sign} (x) \, \frac{1}{1+x^2} = 0 \, .$$ Indeed ...
user avatar
  • 257
1 vote
2 answers
47 views

need dimension of solution space of system of non-linear complex equations

I've been trying to do this in Mathematica for several days but I'm getting almost nowhere. I need to know the dimension of the solution space of each of the two systems of nonlinear complex equations ...
user avatar
  • 11
2 votes
4 answers
255 views

Integral of a real function giving a complex result

Why, when I compute the following integral $$ \int_{0}^{\alpha}dx\int_{0}^{\alpha}dy\frac{ln|x-y|}{\sqrt{(\alpha-x)(\alpha-y)}} $$ for $\alpha>0$, by executing the following: ...
user avatar
  • 755
1 vote
2 answers
232 views

How to expand this integrand as a geometric series and evaluate it?

I study Riemann's Zeta function. This connection between these two functions (Zeta and Gamma) should become clear via the derivation of a so-called functional equation. Starting point is this integral ...
user avatar
  • 649

1
2 3 4 5
24