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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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Interesting output in Integrate [on hold]

I found interesting behaviour, best illustrated in the following example. When trying to evaluate Integrate[1/(d^2 - 1), d] Mathematica 11.3 gives the following ...
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1answer
64 views

Sharp jagged lines in Plot3D

I have the following function of five parameters of which I would like to construct a 3D density plot using Plot3D ...
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2answers
27 views

Different styles for different points in ComplexListPlot?

I'd like to use ComplexListPlot to show a point and its image under a complex function, with the point and image having different styles, say different colors. Use,...
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0answers
35 views

Сontour integral [migrated]

everyone. Can you help with the task?
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1answer
35 views

Plotting Complex Numbers as “Arrows” on the Complex Plane

Given the following complex numbers (defined as the values of two functions f and g defined only on the points ...
2
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1answer
81 views

Taking real and imaginary parts after reciprocal

I noticed the following strange scenario. When I defined a variable to be real, Mathematica does not only recognize that it is real after taking an inverse. How can I resolve this so that it will ...
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1answer
42 views

Adding degrees to complex numbers

I'd like to take the complex number $(1 + 0i)$ and (i) multiply it by $0.5$ and (ii) add 45 degrees to it (without changing its magnitude). But I'd like to get its complex represenation in non-polar ...
0
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1answer
53 views

Showing a specific (complex) point in a Graphic [closed]

Somewhat related to a previous post that I made - Complex infinity at a point and division by zero I'm still following the book on this example and I've come to the part where one draws the '...
2
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1answer
40 views

Discolored ComplexPlot ColorFunction [closed]

I have this code. ...
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1answer
43 views

Complex infinity at a point and division by zero

Edit: I've found out that the book was written for Mathematica 7, which was a pretty long time ago. It boils down to changes in syntax most probably, but simple renaming to lower lettercase does not ...
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0answers
25 views

Expanding the complex conjugate of a Mathieu function as a series

In my calculations, I found this equation: ...
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1answer
35 views

Can we make a labelled parametric plot in which the parameter is integer? [closed]

Can we make a labelled parametric plot in which the parameters are integers? I'm just using Wolfram Alpha but could equally use Mathematica Online, and want something like here. I want to plot ...
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0answers
68 views

How can I get Mathematica to recognize that $ab^* + ba^* = 2\Re(ab^*)$?

Mathematica understands that $z + z^* = 2\Re(z)$, FullSimply[z + Conjugate[z]] (* output: 2 Re[z] *) However, Mathematica does not simplify the expression ...
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1answer
38 views

Complex Exponentials to Trig Functions?

I have an expression expr = 1/2 a E^(-3 I ω t) (E^(3 I ω t)+2 Cos[π x/a]) (1+2 E^(3 I ω t) Cos[π x/a]) Sin[π x/a]^2; expr // TeXForm $\frac{1}{2} a e^{-3 i t \...
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2answers
114 views

How to show that $f(z) = z^2 + 1$ intersects the line through the roots of $f(z) = 0$ in ComplexPlot3D?

I have plotted the complex function $f(z) = z^2+1$ by using the following code: ComplexPlot3D[z^2+1, {z, -5 - 5 I, 5 + 5 I}] However, I want to show that $z^2+1$ intersects the line $\Re(z) = 0$. ...
0
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1answer
68 views

How to plot the complex function $f(z) = z^2 + 1$ in a three-dimensional plot with colouring?

I've noticed that there are different ways to plot a complex function. What I am interested in, is a three-dimensional plot with colouring of the complex function $f(z) = z^2 + 1$. Here is an example ...
3
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1answer
207 views

Using Im[] and Re[] Correctly

Hi I just want to check my code is working properly as I am trying to rule out any errors. I'm integrating 4 coupled ODE's that have real and imaginary terms, so I have 8 equations. The section of ...
0
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1answer
49 views

Finding the negative real root of in set of solutions under a varying constraint

Suppose I have a function and its derivative like: V = x^3.5 - x*y Vx = D[V, x] I first solve V for ...
3
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1answer
116 views

Finding the maximum real part of roots

Suppose that I have this problem ...
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1answer
68 views

Plotting $f: x + i\,y \mapsto u + i\, v$ with Plot3D and mapping $v$ to color

Mathematica already has ComplexPlot3D that plots ReIm[x, y] against Abs[f(z)] and ...
2
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2answers
627 views

Weird result in complex limit

I am trying to evaluate a limit: gamma[w_] = Sqrt[-(u*e)w^2 + I*(u*s)w]; Limit[Re[gamma[x]], {x -> DirectedInfinity[1]}] I calculated the limit by hand, and ...
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0answers
77 views
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2answers
811 views

Why does Arg'[1. + I] return -0.5?

From the document we know that Arg[z] gives the gives the argument of the complex number z. Then how about ...
-1
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1answer
89 views

ComplexPlot3D and essential singularities [closed]

I am trying to understand the behavior of the functions $$ f(z) = e^\frac{1}{z} \qquad \text{and} \qquad \frac{1}{f(z)} = \frac{1}{e^\frac{1}{z}} $$ in the neighborhood of $z=0$. From the power ...
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0answers
29 views

Discontinuities in taking the roots of a complex function

I have the following functions e1, e2, and e3 which consists of the functions ...
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0answers
23 views

Integrating System of ODE's

I'm trying to integrate the system $$\frac{d}{d z} \left[ \begin{array}{l}{\hat{a}} \\ {\hat{b}}\end{array}\right]=\frac{i \omega}{\overline{c}} \left[ \begin{array}{cc}{\left(\Delta_{l}^{(+)}-1\...
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0answers
56 views

Efficient evaluation of real/imaginary parts of long expressions

I have the following, rather compact, but complex, expression (see below). I simply want the real part of this. Now, when I do the usual, i.e., ...
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2answers
79 views

Result with assumptions contradicts previous result

Without assuming anything on the argument of the complex number inside the Gamma function ...
1
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1answer
31 views

Mathematica is not simplifying trignometric functions under Abs although I provide assumptions

I am trying to simplify a simple expression, (1/2)*((-Pi)*Abs[Sin[t]] - Pi*Abs[Sin[t - 2*Pi]] - 2*Pi*Abs[Sin[t - Pi]] + 4) i.e $$ \frac{1}{2} (-2 \pi \...
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2answers
65 views

Taking absolute value of complex variable

I'm trying to take absolute value squared of certain objects. Say I have y=alpha and I know that |alpha|^2 = alpha*Conjugate[alpha]. How do I take Abs[y]^2 ...
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1answer
82 views

How to define a complex function with assumptions?

I'm trying to define a complex function to be able to do analytic calculations. Specifically, I want to define a function $A(x,t)$ in the complex plane with argument $\theta(x,t)$ and modulus $R(x,t)&...
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3answers
391 views

Finding and visualization of branch cuts and branch points

Is it possible to determine branch cuts and branch points for complicated functions using mathematica Iam trying to determine the brnach cuts and branch points of this complicated function We have ...
1
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1answer
54 views

Find roots of transcendental function in regional complex plane

I want to know how many roots does the following equation have and how to solve them all. $f(z)=\frac{\text{sech}(35.0937 x)}{\left(e^{70.1873 x}-1.\right) x} \left((0.\, +0.0235822 i) x^2 \exp \...
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3answers
76 views

How to take a derivative of a function with a real part taken

Consider f[x_]=Re[x^3] I now take the derivative of this D[f[x],x] and the result is ...
4
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4answers
196 views

How to find image of a complex function with given constraints?

I am very new to Mathematica. I have started learning it only last month. I would like to graph the image of some complex valued polynomials with some provided conditions. For example: $$ p(z_1,z_2,...
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1answer
105 views
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1answer
64 views

Complex number as the result of an integral [closed]

My question has been asked before by other members, however, I didn't find the answer to their question helpful in my case. I'm doing a simple numerical integral with real numbers in mathematica, but ...
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2answers
70 views

Numerically integrate complex valued function of a real variable and a complex variable

I need to numerically integrate a complex valued function of a real variable and a complex variable by the real variable. My integral: $$ \int^1_{-1}\frac{e^{ix}}{x-z}dx ~~~\text{where} ~~x \in \...
4
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1answer
138 views

Imaginary part of expression too difficult to calculate

I am trying to calculate the imaginary part of a long expression. It's a long enough expression that Mathematica "hangs" when you run: ...
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3answers
55 views

How can I reduce my work to get the result automatically?

I want to find the locus of point present of the complex z so that $$|z + 2| + |z - 2| = 18. $$ I tried by hand ...
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1answer
93 views

Can you plot complex maps? [closed]

I want to plot $|z+1|=|z-2+i|$/ Is there any way to do this without converting it to Cartesian form and contour plotting?
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2answers
75 views

How to Chop parts of an expression?

The following expression has four terms $T1$, $T2$, $T3$ and $T4$, such that the totalFunction = T1 - T2 - T3 + T4;. It turns out that the part T1-T2 gives a ...
7
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3answers
225 views

Obtaining a matrix of complex values from associations giving the real and imaginary parts of each element?

I have a list of associations keyed by real and imaginary numbers, like so: ...
10
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3answers
689 views

How to use Mathematica to do a complex integrate with poles in real axis?

I want to use Mathematica to compute the following complex integral: Integrate[Exp[I z ] 1/z, {z, -Infinity, Infinity}] Mathematica reports that it does not ...
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1answer
55 views

Conditional Plot of a function if another function satisfies something and in the case of complex variable

Let's say we have function $g(\zeta)$ and another map $f(\zeta)$, where $\zeta$ is a complex variable. I am trying to plot a graph of $f(\zeta)$ but given the condition of $g(\zeta)$. For instance, ...
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3answers
52 views
0
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1answer
64 views

How to collect the real and imaginary parts and make it into two equations

I have an equation which consists of a real and complex quantity I just wanted to separate it out and form two new equations. ...
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2answers
251 views

Complex continuation of an interpolated function

Context I have a complicated real function defined implicitly by a series of imbricated numerical integration. I need to make a continuation of this function for a complex variable which is easily ...
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2answers
73 views

Why does this replacement rule for imaginary unit not work? [closed]

I'm trying to replace imaginary unit in an expression with a real unit: E^(-I y) /. I -> 1 E^(-I y) As you can see, in ...
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0answers
29 views