# 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 ...
33 views

### 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]:-)
34 views

### 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. ...
41 views

We have: 1 + 2 I + 3 + 4 I // Head Complex and 1 + 2 I + 3/5 + 4/5 I // Head Complex But we get: ...
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, ...
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 ...
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 ...
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 ...
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 ...
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? ...
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 ...
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 ...
50 views

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

So I am trying to solve the following polynomial ...
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 ...
35 views

### Integrate returning complex values

I am having trouble using mathematica to calculate some integrals Namely this : ...
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: ...
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) ] ...
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 ...
67 views

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### 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 ...
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 ...
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 ...
37 views

### Get modulus and plot complex function

I have the following function: ...
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 ...
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 ...
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 ...
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 ...
52 views

### Split complex equation

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

### Two different values of the same integral

My question is straightforward. I am getting two different values for the same integral. ...
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 ...
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 ...
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 ...
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]] ...
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 ...
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?
Trying to solve $f(z)=\frac{1}{2^z}+\frac{1}{3^z}$. How can I solve it for complex $z$?