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.

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Solution… 2nd Transcendental Equation with Graphical method [closed]

If $ 2x^3 + \ln x = 5 $, then what is $ x $? For beginning we started to find a solution for equation $$ \begin{align}\label{eq:eq} \ln x + cx = b \tag{1} \end{align} $$ We know from W function ...
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2answers
108 views

Replace $ z z^* $ by $ |z|^2 $

I have a long expression involving different complex numbers. I want to force Mathematica to replace z Conjugate[z] by Abs[z]^2 ...
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1answer
57 views

Is there a function to solve a complicated event probability problem? [closed]

I need to find the probability of this beast: P[(ABEF)+(CDEH)+(ABEI)+(CDEI)+(ABEJ)+(CDEJ)]. A,B,C, etc. represent events with probabilities close to 0.5 so I don't think rare event approximation can ...
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3answers
264 views

Problem of `Integrate` and `DSolve` with inhomogeneous Legendre differential equation

I have the following inhomogeneous Legendre differential equation $(m=n=2)$: ...
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1answer
34 views

Defining 3rd variable for parametricplot3D of two-variable complex function

I am trying to make a parametricplot3D curve of the function Psi(x,t) shown in the included image. My code is the following: ...
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2answers
189 views

Portion of Curve Omitted by Plot

In the course of addressing question 104559, I encountered the following problem with Plot. Begin with ...
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2answers
117 views

How to make $\mathrm{Abs}[x + y\, I]^2$ produce $x^2 + y^2$? [duplicate]

I want to get x^2 + y^2 by evaluating Abs[a + b I]^2. Unfortunately, Mathematica just reproduces the same ...
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0answers
140 views

How to obtain left and right eigenvectors of a general complex matrix with degenerate eigenvalues?

I'm looking to obtain the left and right eigenvectors of a general complex matrix. The left eigenvectors satisfy the equation: $\phi^L_i L = \lambda_i \phi^L_i$, with $\lambda_i$ being the $i$th ...
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2answers
128 views

How to efficiently evaluate Exp[I m θ] [closed]

The I is imaginary number. My question is when m becomes large and the number of θ increases, how to evaluate it faster. Here is one way to get the result and store all the value it found. ...
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2answers
227 views

Simplify product of complex numbers

I am trying to take product of a complex number with its conjugate. When I take A*Conjugate[A] // FullSimplify The output is as desired ...
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0answers
270 views

Plot real and imaginary part of function

I have the following function: f3 = (99. (2154.43 - 100. lh^2.))/lh^1. - (0.0609773 ((2154.43 - 100.lh^2.)/lh^1.)^7.30317)/(-4.64159 - lh)^6.30317 If I plot it, ...
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1answer
354 views

Square root of complex numbers

This is a pretty simple issue with Mathematica but I could not find any previous discussion on this topic. The issue arises when we have fractions as indices of complex numbers. For e.g. Let's say we ...
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1answer
157 views

How to convert this complex number to exponential form? [closed]

I have $Z = {\frac{2+i}{2-i}}$. I need to write it in exponential form, i.e. $Z = r*e^{i{\phi}}$. I simplified the given example to ${\frac{3 + 4i}{5}}$, i.e. $a={\frac{3}{5}}, b={\frac{4}{5}}$. ...
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2answers
95 views

Solve the complex equation z^2 + ((2 + i)/5)z + 1/11 == 0 [closed]

I have tried to solve this in mathematica but cant find the right way. I used ComplexExpand[z^2 + ((2 + i)/5) z + 1/11] which gave the result ...
2
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0answers
33 views

Specifying different thickness for each graded contours of Mandelbrot Set so that I can export it as .STL file.

I am using Mandelbrot Set function in Mathematica to get the Mandelbrot plot. I want to 3d print this model, so want to specify thickness for each contour and then convert into .STL file. Is this ...
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1answer
83 views

Finding the real part of a complicated complex expression

I've the following code: ...
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1answer
112 views

Can this integral be calculated using Mathematica?

I have the following integral: $$ \int_{-\infty}^{\infty} \frac{\mathrm d\tau}{2\pi \mathrm i} \int_{-\infty}^{\infty} \frac{\mathrm d\tau'}{2\pi \mathrm i} \frac{\mathrm e^{-c^2(\tau - \tau')^2}}{(\...
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0answers
61 views

How to use “Chop” kind of operation on whole mathematica file

In an array of steps including logarithms and integrations, I am finding the problem of small imaginary parts of some o/p's which are complicating/inhibiting the further steps. I found that "Chop" ...
8
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3answers
649 views

How to recover Pauli matrices properties in Mathematica?

I want to do a cross or dot product involving a vector of Pauli matrices $ \vec\sigma=(\sigma^1, \sigma^2, \sigma^3) $; for example, $ \vec\sigma\times\vec\sigma=2\mathrm i\vec\sigma $ and $ \vec\...
2
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1answer
155 views

Re and Im relationships without Abs among Fourier, FourierTransform, InverseFourier, and InverseFourierTransform

Is there a way to make Fourier's Re and Im components separately track the results of ...
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0answers
56 views

Force a function to be real

I have a multivariable function in Mathematica that arises as an eigenvalue of a matrix. It involves square roots of the variables involved, but Mathematica automatically assumes such a function to be ...
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2answers
81 views

Problem in dealing with Sign function

Let my function be $f(x)=e^{|x|}$. I wish to find $f''(x)$, this can be done as- $f'(x)=$sgn$(x)e^{|x|}$ $f''(x)=$sgn$(x)^2e^{|x|} =e^{|x|}$ In Mathematica, I am trying to plot $f''(x)$, it ...
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2answers
94 views

Working with complex valued functions

I have a function which has real and imaginary parts and I need to differentiate both parts separately. This is a simpler example of what I have tried, without success: ...
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0answers
39 views

How can plot absolute inequality in complex number

I am new to Mathematica and i would like to know how to plot a complex function.. I cant plot absolute inequality...
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1answer
60 views

Plotting complex number error… |z−2|<1

z[x_, y_] := x + yi f[z_] := {1/(z - 1)}; RegionPlot[{(x - 2)^2 + y^2}^1/2 < 1, {x, -100, 100}, {y, -100, 100}] |Z−2|<1 I am new to Mathematica and i would ...
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1answer
55 views

Roots of an expression

I have an expression as $1 - 2 \sqrt{1 + i r} + i r$, where $r$ is real. I want to find the roots of its imaginary part. So: ...
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3answers
5k views

Visualizing a Complex Vector Field near Poles

I've been playing around with a visualization technique for complex functions where one views the function $f: \mathbb{C} \rightarrow \mathbb{C}$ as the vector field $f: \mathbb{R^2} \rightarrow \...
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1answer
80 views

Using “if” to compare 2 expressions (Complex and real numbers)

Hello. I want to solve this cubic equation and compare the answers then I can assing the lower result to "VmL" and the greatest result to "VmG" but I have problems when the result is a complex number ...
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3answers
3k views

How can I recreate Trott's Riemann Surface plot in Mathematica?

In reading Michael Trott's Visualization of Riemann Surfaces of Algebraic Functions, he has: ...
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1answer
53 views

Failure to plot a subset of curves using ParametricPlot

I wish to plot a parametric curve with parameters Γ,Δ,ϵ such that ...
2
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1answer
51 views

How to declare derivatives of a multivariable function as real in order to get Re and Im part of the expression?

Re and Im work properly, with appropriate assumptions, in the example like this ...
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6answers
801 views

Is there a workaround for this integral?

The command Integrate[Exp[a*Exp[I*x]], {x, -Pi, Pi}] produces ConditionalExpression[0, a == 0] which is not correct in view of ...
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0answers
36 views

Residues of products

i have the following problem: My function is given by: $(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$, ...
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2answers
138 views

Forcing complex output to take the form $a + b\,i$

Solving the complex equation $z^2=1+2\,i$ using Solve[z^2 == 1 + 2 I] returns $\left\{\left\{z\to -\sqrt{1+2\,i}\right\},\left\{z\to\sqrt{1+2\,i}\right\}\right\}$...
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1answer
416 views

How to plot complex eigenvalues of a matrix?

I have a matrix , for instance, like this : matrix[a_ ] := {{0, a}, {-a, 1}}; Eigenvalues[matrix[a]] and this give the eigenvalues that depends on ...
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1answer
39 views

Manipulate function not working possibly because of Arg?

I have the following function eigen1 = 1/3*(p + sig - u2/(2^(8/3)*sig) - 3*I*ω); Where ...
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2answers
97 views
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4answers
71 views

Problem with particular simplification of complex function under assumptions

I have proven that $expr=(1 - i)(\dfrac{1+z}{1-z})^{1/4}\dfrac{\sqrt{ 1-z^2+i z\sqrt{1 - z^2}}}{1+z-i\sqrt{1 - z^2}}=1$ when it is assumed that $z\in R$ and $|z|<1$ and when I also plot the real ...
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1answer
245 views

Evaluate sum of complex exponentials using Kronecker delta

Commonly in e.g. condensed matter physics one encounters sums of the form $\sum_{n=0}^{N-1} \sum_{k} A_k \mathrm{exp}[i\frac{2\pi}{N} kn ]$ where $k$ is summed over all integers in the range $[(-N-...
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1answer
366 views

Eigenvectors normalization

When eigenvectors are real, they are normalized to 1. How are complex eigenvectors normalized?
8
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3answers
1k views

How to make denominator of a complex expression real?

I searched around, but couldn't find any, please help. For example, I got this: $$ -\frac{i}{2 \pi (-i \gamma +\text{V0}+\Omega )} $$ Which command will yield this result: $$ -\frac{i \gamma +\text{...
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0answers
63 views

Why won't Mathematica Conjugate this expression>

I've been trying to replicate the derivation of Bloch's equations in Mathematica and for the final substitution, it won't correctly conjugate the expression even though I specify that all of the ...
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1answer
77 views

Why Does Mathematica Have Trouble Plotting This?

I'm trying to Plot something relatively simple: ...
2
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2answers
90 views

Incorrect result for the region of convergence of a simple integral

Bug persisting at least through version 11.3.0 The standard Gaussian integral Integrate[Exp[-a x^2], {x,-Infinity,Infinity}] returns ...
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1answer
76 views

General result from Integrate differs from result with special values

Can someone explain why these outputs differ? ...
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1answer
81 views

Distributing complex conjugate

If you have a statement like: Conjugate[a+b] you get back Conjugate[a+b] but I'm expecting ...
2
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0answers
86 views

Real integral giving complex result [duplicate]

I'm trying to calculate the following indefinite integral: $$ \int \log \left(\left(\frac{\lambda ^2}{a \lambda ^2+b}+\text{$\Delta $0}\right)^2\right) \, d\lambda $$ which is producing the ...
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1answer
61 views

How to create a colour picture?

Hope to have a composite colour graphics after I put in complex number, part of t=1 is a color,part of t=2 is another color,and so on. Maybe my function is not good. How to fix it? Thanks a lot! ...
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1answer
39 views

Mathematica not recognizing expressions are real

I see no problem with following calculation. Refine[ComplexExpand[b I /(a + b I)], {Element[a, Reals], Element[b, Reals]}] ...
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2answers
83 views

how can I define a symbol as a global real number?

Say there is a complex number a=x+I, where x is a real number. Then b=Join[{a},{1+I}], and I ...