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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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1answer
78 views

ComplexPlot3D and essential singularities [on hold]

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 ...
1
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0answers
23 views

Discontinuities in taking the roots of a complex function

I have the following functions e1, e2, and e3 which consists of the functions ...
0
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0answers
22 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\...
1
vote
0answers
54 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., ...
0
votes
2answers
77 views

Result with assumptions contradicts previous result

Without assuming anything on the argument of the complex number inside the Gamma function ...
1
vote
1answer
25 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 \...
1
vote
2answers
56 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 ...
1
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1answer
63 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)&...
12
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3answers
334 views

Finding and visualizing 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
46 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 \...
1
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3answers
73 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 ...
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0answers
52 views

Packages or rules to simplify complex expressions

I am currently trying to simplify a very complicated looking expression, which is a function of four angles $\theta_{i}$ and one real variable $t>0$. Naively doing PowerExpand I get relatively ...
4
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4answers
193 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,...
1
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1answer
103 views
0
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1answer
54 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 ...
0
votes
2answers
53 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
votes
1answer
133 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: ...
1
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3answers
52 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 ...
0
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1answer
87 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?
0
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2answers
74 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
224 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
votes
3answers
664 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 ...
0
votes
1answer
41 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
49 views
0
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1answer
52 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. ...
7
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2answers
216 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 ...
1
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2answers
67 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 ...
0
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0answers
28 views
0
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1answer
34 views

Finding complex conjugate [closed]

I have some expressions and I would like to calculate the complex conjugate of them. How can I get delta2 and delta3 in a simple ...
1
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2answers
48 views

Find n-roots of unity and put them in vector [closed]

Assume you want to find all roots of n-unity and then you want to put them in a vector. I tried to find all the roots of unity this way: Solve(z^n==1,z) But now ...
0
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2answers
36 views

Simplifying complex-valued entries in a matrix

I have a matrix where some entries are complex or roots of unity. For example, (-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9) is one such entry and it is equal to 0. ...
3
votes
2answers
88 views

Complex solutions to ODEs

How do I solve the following IVP problem in Mathematica so that I get real solutions? $Q'(t)=b - \dfrac{Q(t)}{100-t}; \quad Q(0)=250$ I tried the following: $\text{$\$$Assumptions}=b>0;\text{$\$$...
1
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0answers
33 views

Inverting a series

How do I invert the following, \[Rho]=r + b0 Sum[Pochhammer[1/2, k]/(k! ((1 - q) k - 1)), {k, 0, \[Infinity]}] + b0^(1 - q)/(2 q) r^q + O[r^(2 q - 1)] to get $r(...
6
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0answers
57 views

Where is the mistake in computing the particular eigenvector of the following DFT Matrix?

I have the following matrix (the DFT Matrix for N = 3) $$W = \frac{1}{\sqrt{3}}\begin{pmatrix} 1 & 1 & 1 \\ 1 & e^{-\frac{i 2 \pi}{3} } & e^{\frac{i 2 \pi}{3} } \\ 1 & e^{\frac{...
2
votes
2answers
93 views

`Re[z]` Command [closed]

Suppose we have complex number $z=a+i b$, where $a$ and $b$ are variables. Now, if we want real part of $z$, then in mathematica we use Re[z] command. But this ...
0
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0answers
51 views

double Integral in complex number field

The following expression is an expansion of Hypergeometric2F1 function from the above expression with the help of 9.113(in 'Table Of Integrals, Series And Products'). but I got different results.WHY? ...
6
votes
2answers
153 views

Does Mathematica gives us a wrong result for the integral of a function including elliptic functions?

Calculus tells us that the differentiation of the integral of a function should be itself, but at least in one case Mathematica answers NO. I feel very confused. The new figure seems to bifurcate at ...
3
votes
1answer
109 views

Complex first-order differential equation

I have a differential equation $\frac{dx}{dt} = \sqrt{1+x^4}$ $x$ is a complex variable. I want to solve it for some given initial condition, and plot the solution (real part vs. imaginary part). ...
2
votes
1answer
56 views

Choose a branch cut using assumptions

I understand Sqrt function won't simplify expressions such as $\sqrt{x^2}$ unless there is an assumption that $x \in \mathbb{R}$. In my computation, I get an output containing an expression like this ...
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3answers
140 views

Gives me a complex solution [closed]

A := DSolve[{D[((It - Ir) * x / L + Ir) * w''[x], {x, 2}] - p/Y, w[x] == 0, w'[0] == 0, w''[L] == M0/(Y*Ir), w'''[L] == -P/(Y*Ir)}, w[x], x] I want a real ...
10
votes
1answer
190 views

FiniteElement v.s. TensorProductGrid: which is reliable for Schrödinger equation with periodic b.c.?

This is a problem comes up in the discussion under this post and I think it's worth starting a new question for it. I suspect the underlying issue is the same as in this post, but not sure. Consider ...
4
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3answers
135 views

Conjugate & Derivative

I have some problem with the derivative of the 'conjugate' expression: Here I define the functions: ...
2
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0answers
62 views

Speed up Mathematica's Simplify and ComplexExpand functions

I am trying to simplify an expression and taking the real part only. However Mathematica use ages to run the command (if it is able to do so in the end). The problem is that the expression I am ...
0
votes
3answers
69 views

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 ...
3
votes
2answers
106 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 ...
0
votes
1answer
54 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 ...
3
votes
1answer
156 views

What does “ Im' ” mean? [closed]

I am trying to take the curl/derivative of the function A. What does " Im' " mean here? Why does Mathematica attempt to take the derivative of the Im function here? ...
0
votes
0answers
74 views

An optimization problem

I have the following two quantities denoted by $LHS$ and $RHS$: ...
2
votes
2answers
113 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 ...
0
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0answers
94 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 ...