# 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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35 views

### Plotting partial sum with complex number

$$\sum_{n=1}^{N} e^{2\pi in\sqrt2}$$ We have to use Accumulate and ListLinePlot, and my implementation so far with upper bound ...
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### Best way to solve for domain on which a function is real

Say I have a function like ...
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### How to specify domain? [closed]

I wrote x $\in$ Reals; y$\in$ Reals; z = x + I y; Re[z] gave the output -Im[y] + Re[x] as if the first line did not exist How can I specify that x and y are reals?
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### Solve a system of complex equations and plot the solution

I'm trying to solve a system of 2 equations with an unknown real parameter k0, the solution is complex. then I want to plot the obtained solution function of k0: here is my code: (I here is the ...
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### Plotting Minkowski product of two sets in complex 2D plane

I am trying to draw Minkowski product of two sets in complex 2D plane in Mathematica. While I can draw the individual complex 2d plane for these sets in Mathematica ...
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### Complex mapping of curve

I have a curve in the complex plane (a unit circle), and I want to plot the curve with a complex function applied to it ($f(z)=\sqrt{z}$) How do I go about doing that? I know how this can be done ...
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### Why does Abs return negative values?

According to the documentation Abs[z] gives the absolute value of the real or complex number z and is also known as the modulus. As far as I'm aware for any definition of the absolute value, norm or ...
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### Stopping Simplify and FullSimplify expressing real terms as complex

I am working with real functions but FullSimplify and Simplify express them as complex terms. I assume this is because the ...
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### Why does Log[Abs[#]] return a complex number?

For a nonzero number $x$, $\log|x|$ should be a real number. Why does the following NestList contain non-real numbers when no numbers involved are close to zero? Is it a bug? ...
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### Using callout[] to create a plane

I want to create a plane that represents $15$ powers of complex number: $a$1 $= (10/7)*(Cos(Pi/10) + i*Sin(Pi/10))$. I also want to label the points with the text "a to power k" where $k$ ...
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### 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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### 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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### 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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### 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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### 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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### 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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### Pattern-matching complex numbers as a + bi

I just started working with Mathematica and am toying with pattern matching. There may be something obvious I'm missing in this, but I can't figure it out by myself. I want to write down a function ...
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### 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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### 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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### 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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### 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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### Returning complex numbers when it's supposed to be real numbers

So I am trying to solve the following polynomial ...
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### 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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### Integrate returning complex values

I am having trouble using mathematica to calculate some integrals Namely this : ...
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### 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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### 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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### 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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### 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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### 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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### Get modulus and plot complex function

I have the following function: ...
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### 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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### 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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### 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 ...