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
1 answer
28 views

Trouble with Finding a Supremum Constrained by a Condition

I have a function $$ f(x,y) = \sqrt{\left(x^4 y+\frac{2 x^2 y^2}{x^2 y^2+1}+\frac{2}{x^2 y^2+1}-41 x^2 y-7 x^2\right)^2+\left(-7 x^3 y-x^3-\frac{2 x y}{x^2 y^2+1}-\frac{2 x^3 y^3}{x^2 y^2+1}+41 x\...
Martin Strmiska's user avatar
3 votes
0 answers
90 views

Workarounds for unevaluated results of ContourIntegrate of non-analytic functions

There is a new useful command ContourIntegrate since 13.3. I find that the command is well-done, but even the Sun has spots. ...
user64494's user avatar
  • 24.5k
21 votes
2 answers
2k views

How can we reproduce Eugen Jahnke's drawing of a complex function?

Eugen Jahnke (1863 - 1921) studied mathematics and physics at the Humboldt University of Berlin. He became a professor at the Berlin Mining Academy in 1905. His "Tables of Functions with ...
eldo's user avatar
  • 49.2k
3 votes
1 answer
243 views

Absolute value of a complex number [closed]

I want to calculate |xx|^2. Why can't Mathematica just calculate it? What am I supposed to do here? I just want it to actually calculate it, so that there are no imaginary numbers left. Is that so ...
Σ balls's user avatar
1 vote
3 answers
112 views

Plotting |z-2| < 1 under w = z/(z-1)

How can I plot the image of |z-2| < 1 under the transformation w = z/(z-1)? The expected result should look something like ...
internet's user avatar
  • 517
1 vote
0 answers
36 views

How to assume a function is holomorphic?

For example, for a holomorphic function $f(z)=f(x,y)$, it's well know that $\ln |f|$ is harmonic. I want to check it with mathematica with the following code: ...
gaoqiang's user avatar
16 votes
1 answer
642 views

How can we plot Man Ray's "Shakespearean Equation" w == e^(1/z)?

1. Man Ray Man Ray (1890 - 1976) was an American artist who spent most of his career in Paris. He was a significant contributor to the Dada and Surrealist movements. Man Ray produced major works in a ...
eldo's user avatar
  • 49.2k
0 votes
0 answers
23 views

Simplify vector calculus based on component splitting

I am interested in verifying a few Vector Calculus expressions using Mathematica. These expressions are based on splitting a vector field into its transverse components (in the xy- plane) and ...
orlandini's user avatar
4 votes
2 answers
194 views

Complex region plot

How do I plot the following two sets in the complex plane: $C=\{z\in\mathbb{C}|z^4\in[0,16]\}$ and the set of solutions of equation $Re(\frac{2z+1}{z+1})>0$ Thanks in advance.
fasdgr's user avatar
  • 377
2 votes
2 answers
182 views

Real zeros of complex function

I must find the zeros of a complex function $\xi$ that depends upon two real variables $B$ and $k$. The function is obtained by evaluating the determinant of the identity matrix of dimension $2n$ ...
Dario Bercioux's user avatar
0 votes
2 answers
69 views

How Not to Simplify Exponential of Log?

I have the expression Power[x,I y] Both $x,y$ are real. Now I want to write this expression in term of Exponential of Logarithm. The expression can be rewritten as ...
Nitaa a's user avatar
  • 698
4 votes
1 answer
185 views

Implementation of SINC filter using Integrate results in incorrect output

Bug introduced in 6.0, persisting through 13.3.1. This is SINC filter, integrate $|H|^2$ from $-\pi/2$ to $\pi/2$. MMA CODE, Result = 7.27956e-12 ...
Ring's user avatar
  • 127
0 votes
0 answers
51 views

How does Mathematica select principal roots of complex numbers?

When I do I^(1/3) I get Out[]:= (-1)^(1/6) which is one of the solutions of $z^3=i$. There are two more solutions which are ...
sam wolfe's user avatar
  • 4,179
0 votes
2 answers
78 views

How to draw a 3D plot of a function which have two parameters with complex parametric values?

I am trying to draw the 3D figure of the function 1+e^{px+qy} with the complex parametric values p=1+i and q=2-3i. Actually, I am trying to draw a 3D figure of a function of the form f(x,y) = e^{ax+by}...
Uttam Kumar Mandal's user avatar
0 votes
0 answers
61 views

Visualizing conformal map from upper half plane to n-gon

I want to plot both the upper half plane and the image of it i.e. a polygonal region via Schwarz-Christoffel maps. One example is for a quadrilateral. ...
Physics Moron's user avatar
2 votes
0 answers
143 views

Finite sum of complex exponentials giving wrong result [closed]

I was playing with the following sum: $$ \sum_{k=0}^{2} e^{\frac{2\pi i k^2}{3}} = e^{0} + e^{\frac{2\pi i}{3}} + e^{\frac{8\pi i}{3}} \ne 0, $$ which is non-zero, at least according to Wolfram|Alpha. ...
Sidharth Ghoshal's user avatar
2 votes
1 answer
98 views

Level curves of $|e^{1/z}|= s$ for $s \in \mathbb{R}$

In order to find the behavior of a complex-valued function at an essential singularity, I want to plot $|e^{1/z}|= s$ for $s \in \mathbb{R}$, say for $s= 1, 1/2$. Following is the code but it doesn't ...
Eureka's user avatar
  • 123
1 vote
0 answers
108 views

Why ResidueSum returns 2 different values?

I want to calculate the sum of the residues of the function $$ \frac{\sin(\theta)\tanh(\alpha x)}{-\cos(2xL)+\cos(\theta)}, $$ for $|x| \leq1$. The function has singularities at the points $x_n^\pm = \...
Jean's user avatar
  • 11
2 votes
2 answers
155 views

Solve an equation involving Exp over the complexes

I need some help to solve an exponential equation with Mathematica over the complexes. This is the equation I need to solve. I've already used FullSimplify. ...
Marthy92's user avatar
1 vote
1 answer
150 views

How to return only the negative complex solutions of DSolve or using FindInstance?

I am using DSolve to find the solutions to two differential equations. The problem is from the first solution, I only want the solution that includes a negative ...
RudyJD's user avatar
  • 121
0 votes
0 answers
63 views

How do I find the definite double integral of a real number over a complex region?

This is a follow-up question of How do I take the integral of a real number over a complex region? Given that $\tau'$ is imaginary, how would you calculate the definite double integral over a complex ...
Quark Soup's user avatar
  • 1,560
1 vote
1 answer
47 views

How to plot a 3D-subspace of a $\mathbb{C}^2$ curve?

I am trying to visualize the intersection of a complex curve in $\mathbb{C}^2$ with various 3D subspaces but I am not sure how to get Mathematica to do it (so far I have been able to visualize ...
Wolfgangg's user avatar
1 vote
2 answers
133 views

How to simplify expressions with complex exponents?

I have the following expression expr = -E^(-I k) Sqrt[ E^(I k) k1 k2 + E^(3 I k) k1 k2 + E^(2 I k) (k1^2 + k2^2)] with real k, k1, and k2. I want to simplify it to ...
Mohit Kumar's user avatar
1 vote
1 answer
84 views

Numerical integration over Re[expr] still has $0 i$ in the result

I am using NIntegrate to evaluate the integral of the real part of some function. ...
Zhengyuan Yue's user avatar
2 votes
1 answer
136 views

How to plot this set in the complex plane?

I'd like to plot the set ...
user64494's user avatar
  • 24.5k
2 votes
1 answer
82 views

What is the status of ComplexAnalysis`BranchPoints and ComplexAnalysis`BranchCuts?

In 13.3 and I believe quite a few versions earlier I could perform ...
nilo de roock's user avatar
2 votes
2 answers
666 views

How do I take the integral of a real number over a complex region?

If $A$ is a constant, real number with respect to $\tau$ and $\tau$ is an imaginary number, then how would I compute the integral in Mathematica?$$f(\tau)=\int A\space d\tau$$$$\tau=ir$$$$f(r)=Ai\int ...
Quark Soup's user avatar
  • 1,560
2 votes
1 answer
102 views

How to convert DifferenceRoot into a special function?

Clear["Global`*"]; f[z_] := z^(2 m) /(1+z)^m res = SeriesCoefficient[f[z], {z, -1, -1}, Assumptions -> Element[m, PositiveIntegers]] The result ...
lotus2019's user avatar
  • 1,943
0 votes
0 answers
90 views

Missing plot for double derivative with log

I want to plot the given code of double derivate with log function. My derivative is a function of delta P. But when I run the code, I never see the plot. ...
abdul wahab's user avatar
2 votes
0 answers
54 views

Plotting diagram of complex equation [closed]

I have this equation: q1[t_] := -I*γ*Sin[θ] + ((γ*Cos[θ])/n^2)*(I*ξ[t]*y+z*α[t]) and the main code is the following with the definition of each parameters: ...
Ali Taher's user avatar
0 votes
1 answer
54 views

Taking the Unit Disk as a Domain for ComplexRegionPlot

I am very new to Mathematica and overall not very good with programming. I want to plot the region $|(\frac{z}{f(z)}f'(z))^{1+q}-1|<1$ where $z$ is taken from the unit disk and $0<q<1$. In ...
CX Ang's user avatar
  • 1
0 votes
0 answers
65 views

Successive multiplications using Mathematica tools

Successive rotations on the unit circle Given an arbitrary starting point $z$ on the unit circle in the complex plane, the goal is to compute a cycle of rotations by $\pi$/2 with successive ...
dantopa's user avatar
  • 1,050
0 votes
2 answers
120 views

Complex integral with branch cuts

I am struggling with a complex double integral with multiple branch cuts. Even the single variable complex integral I find quite complicated due to the branch cut and the special functions involved in....
Physics Moron's user avatar
2 votes
1 answer
49 views

How to simplify the following expression of a matrix with complex conjugation?

Consider the following matrix: ...
John Taylor's user avatar
  • 4,741
1 vote
0 answers
97 views

Mathematica fails to correctly recognize Hermitian matrix

I have a Hermitian matrix, but Mathematica gives 'False' when I try with HermitianMatrixQ. ...
Sayandip Ghosh's user avatar
1 vote
2 answers
105 views

How to transform a complex quotient involving absolute values and conjugates into the rectangular form?

I am relatively new to Mathematica and I am still trying to figure out all the commands. I have these three complex numbers: And I wish to calculate the following quotient and write it in the a+bi ...
Ihab Alrikabi's user avatar
0 votes
0 answers
52 views

How to correctly represent any Power function and How to draw the image of Power function correctly? [duplicate]

Why is the result of solving this inequality incomplete?Is it a BUG in the software? According to cvgmt's answer to the previous question, I review the function images of Power function again, and ...
csn899's user avatar
  • 2,905
0 votes
1 answer
100 views

Why is the result of solving this inequality incomplete?Is it a BUG in the software? [closed]

Solve this inequality In[41]:= Reduce[x^2 > x^(1/3), x, Reals] Out[41]= x > 1 Missing a solution as x<0 There was ...
csn899's user avatar
  • 2,905
6 votes
1 answer
156 views

Result of numerical computation representing a real physical quantity still contains a small imaginary components [closed]

I have been grappling with a physics calculation pertaining to thin film optics. I have been endeavouring to use transfer matrix calculations to determine optical reflectance. Attached below is the ...
Hooman Puyandeh's user avatar
2 votes
2 answers
59 views

Computing the continuous eigenvalues of a family of matrices

I want to compute the eigenvalues of a family of $2 \times 2$ unitary matrices $M: [0, 2 \pi] \to U(2), k \mapsto M(k)$, which is given by \begin{align*} M(k) = \frac{1}{2} \, \begin{pmatrix} ...
Andreas132's user avatar
4 votes
2 answers
200 views

Simple sum runs endlessly

I tried evaluating Sum[-(1/(2 X (-X+vF (I+y) (I T+n β))^3)),{n,-∞,∞},GenerateConditions->False] which did not terminate. Whereas the modified sum ...
Quasar Supernova's user avatar
3 votes
3 answers
199 views

Given the u or v of the analytic function f(z), find f(z)

Given the u or v of the analytic function f(z), find f(z): z=x+I y, f[z]=u[x,y]+I v[x,y] Given $v=\left[-x+\left(x^2+y^2\right)^{...
lotus2019's user avatar
  • 1,943
1 vote
2 answers
106 views

What is the difference in plots features between analytic (holomorphic) and non-analytic functions?

We know FunctionAnalytic can check whether a complex function is analytic. But I want to use ComplexPlot3D or ...
lotus2019's user avatar
  • 1,943
2 votes
1 answer
103 views

Why does Wolfram|Alpha give inconsistent result for $\int_0^\infty \frac{e^{x-x^2}-e^{-x-x^2}}{x}~dx$? [closed]

Why Wolfram gives inconsistent result for : $$I=\int_0^\infty \frac{e^{x-x^2}-e^{-x-x^2}}{x}~dx$$ As shown in the picture below, the analytical integration gives $-i\pi$, but numerical integration ...
MathFail's user avatar
  • 183
1 vote
0 answers
40 views

Getting hue correct in a complex argument plot [duplicate]

I'm trying to generate a picture of the phase of a complex function defined on a rectangle. I'm using Hue (which is cyclic) and DensityPlot, but it's leaving out certain "corners" of the ...
Bruce Bartlett's user avatar
1 vote
3 answers
143 views

Expanding a complex number

How does one get Mma to expand (1/2 + I/2)/Sqrt[2] into 1/(2 Sqrt[2]) + I/(2 Sqrt[2]) Even evaluating this second expression ...
Mariano Suárez-Álvarez's user avatar
1 vote
2 answers
110 views

Prove complex equation

Assuming $\frac{z_2-z_1}{z_3-z_1}=\frac{z_1-z_3}{z_2-z_3}$, to prove $$ \left|z_2-z_1\right|=\left|z_3-z_1\right|=\left|z_2-z_3\right| $$ ...
lotus2019's user avatar
  • 1,943
3 votes
4 answers
572 views

Prove that the modulus of a complex function is 1

Assuming that both $a$ and $b$ are complex and $| b |<1$, $| a |=1$, I want to prove that $\left|\frac{a-b}{1-a^* b}\right|=1$. My code: ...
lotus2019's user avatar
  • 1,943
1 vote
1 answer
113 views

Conjugating real elements

Facing the same problem reported here: Conjugation with real elements answers are working, I thought of the following solution: ...
geom's user avatar
  • 648
2 votes
2 answers
194 views

Import complex numbers from a CSV file created in MATLAB

I export a simple CSV file created in MATLAB with complex numbers, such as: 0.1+2.1i,0.9+0.13i,0.02+0.3i I would like to import it into Mathematica with the "i" recognized as the imaginary ...
Philipp's user avatar
  • 115

1
2 3 4 5
27