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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22 views

Complex Conjugate Help

I am trying to follow my teacher's instructions to easily compute for a complex conjugate but I get mathematica to actually reveal the complex conjugate besides the word "conjugate" and even ...
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How to enter the imaginary “i” in a text-based interface? [closed]

I use Jupyter/nteract with wolfram language engine. How to input the complex number (1+2i) from the keybord? Im tired of typing Sqrt[-1]:-)
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Why Mathematica is not plotting graph for complex number? [closed]

I am trying to plot graph w.r.t 'r' using Plot command, but Mathematica is unable to plot anything. Sometimes it plot complex number and sometimes not. Please help. ...
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Head of complex sum

We have: 1 + 2 I + 3 + 4 I // Head Complex and 1 + 2 I + 3/5 + 4/5 I // Head Complex But we get: ...
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1answer
63 views

Plotting line segments in complex plane

Recent versions of Mathematica have introduced various functions for plotting in terms of complex numbers and complex functions, including ComplexPlot, ...
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21 views

Why does ComplexListPlot labeling function require an Evaluate?

Start with the list of the cube-roots of unity: cubeRoots = ComplexExpand[Exp[(2 \[Pi] Range[0, 2] I)/3]] I want to use ...
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2answers
103 views

ComplexListPlot: how to add filling lines to origin?

MMA 12. Many XY-style plot functions support the Filling option, so that e.g Filling->Axis drops a line from every plot point ...
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2answers
88 views

Value on the cut

I did the following evaluation (-x)^-a /. {x -> 1.23 , a -> 2.34} 0.296789 - 0.539856 I Now I tried to play around it a bit and did the same evaluation in ...
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2answers
171 views

Can the error function be expressed in terms of other special functions?

I obtained with Mathematica some results written in terms of the error function Erfi[x]. Is there is a way to transform the error function into other special functions e.g. Bessel functions or ...
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5answers
184 views

Simplifying away imaginary part

I'm solving the following eigensystem, and I get result which looks complex-valued. I expect the result to have 0 imaginary part, can anyone see a way to simplify it away? ...
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1answer
46 views

General form of equation [closed]

How do I use a general equation form as a function that calculates my data points of x and y? Essentially, I am trying to use the vernal form equation to calculate conduction velocity from diameter ...
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0answers
41 views

Constant inside If condition

I hope you are doing well. I am currently writing some code in which I have an If statement where I will be dividing two expressions and checking to see if the quotient comes out to be a constant ...
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50 views

Returning complex numbers when it's supposed to be real numbers

So I am trying to solve the following polynomial ...
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1answer
76 views

How to show the map of a complex function ( plane z incl the basic square grid to plane w?

I want to make a presentation of the maps of the standard complex functions, as well as some mobius transformations and special complex functions. I want to present it exactly like it is done in the ...
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35 views

Integrate returning complex values

I am having trouble using mathematica to calculate some integrals Namely this : ...
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1answer
61 views

Solving complex differential equation with ParametricNDSolveValue

I am trying to solve a complex differential equation for the function $S(u,v)$ depending on the parameter $\omega$. The code is: ...
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0answers
78 views

How to convince Mathematica that $(-1)^{2/3} = e^{2\pi i /3}$

I have a list T which contains 3 + 4*E^(2*Pi*I/3). Yet MemberQ[ T , 3 + 4*(-1)^(2/3) ] ...
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2answers
85 views

Symbolic properties of Re and Im

I want to define a function f such that f[x] is real whenever x is real. So I define ...
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0answers
67 views

Prime factorization over the Eisenstein integers $\mathbb{Z}[\zeta]$

I am trying to write a function f[a_,b_] which takes in two integers $a,b$ and returns the unique factorization of $a+be^{2\pi i/3}$ into the primes belonging to $\...
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44 views

Why doesn't Mathematica ComplexExpand integrals?

Consider this code example: ComplexExpand[Re[Integrate[f[t], {t, a, b}]]] Mathematica gives me the result as ...
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3answers
86 views

How to plot a complex functions in complex plane? [closed]

How to plot a complex equation like f(z)=z^2 in complex plane? Is it required to separate the real and imaginary parts or it can be done directly ?
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1answer
43 views

Invalid comparison in Manipulation with Stepwise function

I want to draw a graph of the function that I specified using Piecewise. Though I can draw a graph, I keep getting errors saying invalid comparison with -xx + yy i attempted. The followings are my ...
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1answer
54 views

Assume that the value of an integral is real

I would like to give a condition that the integral I am handling are not complexes. Consider ...
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0answers
63 views

Is there a function to convert a trigonmetric expression to an algebraic expression suitable for ComplexPlot?

According to H. A Priesley: "both $cosθ$ and $sinθ$ can be written as simple algebraic functions of $z$": $cosθ =\frac{1}{2} (z + \frac{1}{z}) \tag1$ $sinθ =\frac{1}{2i} (z − \frac{1}{z})\...
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1answer
54 views

How to get smooth square root of complex valued function?

Let $f(x)$ be smooth complex valued function with real argument $x\in[0,1]$. I want to get square root $g(x)=\pm\sqrt{f(x)}$ where the sign is chosen so that g(x) is smooth. How can I do that? In ...
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1answer
41 views

Is it possible to have a complex nu in ParabolicCylinderD?

I'm trying to recreate a graph from a paper, and the function that I'm plotting involves three separate parabolic cylinder functions that all have a complex Nu value. After getting it all typed out, I ...
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1answer
62 views

Removing Abs with `ComplexExpand` not working

Here is what I have used for this. From this link, Why do I get empty graph when adding 'Abs' function? I know that I can remove Abs with ...
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1answer
37 views

Get modulus and plot complex function

I have the following function: ...
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1answer
66 views

Split real and imag parts of function with derivative

Consider a complex function y with a real argument x and the function y itself is an ...
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3answers
82 views

How to solve these complex equations for plot?

I am trying to Plot this code but it is not showing any plot. I want a bistable type plot between "NL" and "P0" and there are six equations and six unknowns. The code is given ...
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0answers
25 views

How to tell Mathematica to display results in terms of * symbol instead of Conjugate[]

When I have complicated expressions with several complex conjugations, which I write in using the symbolically tidy Esc conj Esc, it frustrates me how Mathematica will then always display ...
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43 views

How do you define the domain and range of the variables for a plot?

How do I define the domain to be only reals and the range to be only complexes? Everytime I plot using ComplexPlot[], I get a C->C function so there are basically too many variables to plot and I ...
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1answer
52 views

Split complex equation

Sometimes it is useful to split a complex equation into its real and imaginary parts. Consider the following ode ...
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2answers
87 views

ContourPlot for a certain value

Consider this example: f[x_] := -I*2*x + 3*x^2 which is a complex function defined on a complex plane $x=x_r+ix_i$ It is convenient to plot the contour of its real ...
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1answer
79 views

How to solve complex equations and plot the graph?

I am trying to solve these equations and want to plot the value of $a^{\dagger}a$ versus P0. I have tried this code but this gives me an error like "Conjunction::argr: Conjunction called with 1 ...
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2answers
63 views

How to get rid of imaginary part in cubic root

When I try to solve the following cubic equation for $a$ on mathematica : S=Solve[a^3 - 4 x - 2 a^2 x + 8 x^3 + a (- 6 - 4 x^2) == 0,a]; I get a complex expression ...
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0answers
41 views

Ordinary differential equation in the real domain

If I have the following equation (y - 1) ^5 == 32 I can select the real solution with Solve[(y - 1) ^5 == 32, x, Reals] Now, I ...
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1answer
88 views

Coding the Mandelbrot Set for Beginners

I'm new to Mathematica and will need some help in coding the Mandelbrot set. I don't want to use MandelbrotSetPlot since I want to understand the interior ...
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1answer
44 views

Symplifying expressions with exponentials inside square root

I have an expression $$ \exp (i k x) \sqrt{y^2 \exp (-2 i k x)} $$ When I put this in Mathematica and do FullSimplift, it gives ...
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0answers
42 views

What are “VariableReplacementDump” and “TranscendentalDump”?

I have run into a Mathematica object I've never seen before and Googling those reveals nothing. I'm talking about VariableReplacementDump and ...
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1answer
63 views

How plot this list in ytg[y,t] axes

I have a list of complex numbers in the form of g[y,t] such that {y,0,1, .1},{t, 0,1, .1}. How can I plot this list in ytg[y,t] axes ...
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1answer
101 views

Two different values of the same integral

My question is straightforward. I am getting two different values for the same integral. ...
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1answer
30 views

Labeling the ticks on the imaginary axis with multiples of i in ComplexListPlot

I would like to have the ticks on the imaginary axis of a ComplexListPlot to be labeled with $-2i$,$-i$,$0$,$i$,$2i$ instead of $-2$,$-1$,$0$,$1$,$2$. I have ...
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0answers
35 views

ComplexExpand in Module doesn't work as it should, when there is function at the left

I'm new with mathematica and I'm having a problem. I hope you can help me. I made a module to built a system that I can use to find some condition for given polynomial is a Shur polynomial. (Actually ...
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79 views

How to have a 3d plot of a complex polynomial?

I'm trying to have a 3d plot for a complex polynomial using the ContourPlot3D It shows me a plot which does not vary when the input values of different variables are varied. So, I guess it is just a ...
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1answer
24 views

Simplify Difference of Conjugate Pairs

Is it possible to easily simplify the difference of conjugate pairs? In particular, if there's just a single variable, then FullSimplify[a - Conjugate[a]] ...
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3answers
224 views

Multiplying two complex SparseArray objects, yielding empty SparseArray crashes kernel

Problem: When I multiply together two sparse matrices that should give back the 0 matrix, where at least one element among the two is complex and at least one is not an exact number, the kernel ...
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1answer
67 views

Square root of a matrix with complex elements

How to compute the square root of the matrix Rho = {{Wxx, Wxy, Wxz}, {Wyx, Wyy, Wyz}, {Wzx, Wzy, Wzz}} if not all of its elements are real?
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1answer
45 views

Simplifying complex expresion (without ComplexExpand or User defined rules) [closed]

Many times, I've struggled with simplifying complex expressions, such as this extraordinarily simple expression, and Mathematica wont do it: ...
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1answer
58 views

Finding zero of complex function

Trying to solve $f(z)=\frac{1}{2^z}+\frac{1}{3^z}$. How can I solve it for complex $z$?

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