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
77 views

How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
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0answers
38 views

Why is PolyLog[] giving weird answers for ordinary values?

Possibly related to this question, but it seems slightly different: Strange behaviour of PolyLog Function Wikipedia says that for real s, z<1 should be real. So I was confused when MMa returned: ...
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1answer
42 views

Plot of the set complex numbers [duplicate]

I want to show this set (eigenvalues of my matrix): ...
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0answers
42 views

Complex input for Compile makes it slow

I asked a question here and then tried to use Compile for the solution to gain even more speed. Inside Compile there is a loop ...
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1answer
77 views

Matrix form of complex numbers [closed]

Complex numbers have matrix form. But some 2x2 matrices while differ, represent the same complex number. To compare complex numbers one has to transform the matrices to the form \begin{pmatrix} a ...
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1answer
82 views

Is it possible to have Logarithm with base 1 or 0? [closed]

I am wondering is there any definition that allows logarithm to have base 0 or 1 in real or complex fields (considering Euclidean space)?? Out-coming question is if you can define a logarithm with ...
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1answer
54 views

Evaluating the real part of an expression

I want to get the Real part of this expression - shouldn't be too hard to evaluate. Why is Mathematica not evaluating but returning the same code? ...
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2answers
200 views

How to tell Mathematica that certain variables are real/imaginary, integer-valued, etc

I'm trying to expedite some quantum mechanical calculations by running them through Mathematica. Expectation values and stuff like that. When I say, for example, ...
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1answer
68 views

How do I declare that a variable represents a real number?

How do I tell Mathematica that a variable is a real number. I searched for this question here and in Google and nothing that was suggested seems to work for me. I must be missing something. My code is ...
4
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1answer
165 views

Problem on limit involving complex numbers

I have $${\frac{(6 k+1)^{k}}{(2 k+5)^{k}}}*(z-2 i)^k$$ and I need to find it's limit for $k$ approaching infinity. ...
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1answer
73 views

Why is it so complicated to simplify a complex conjugate? [closed]

My question is very simple. I would like to multiply a complex number by its conjugate. Unfortunately, this seems to be extremely complicated in Mathematica. Consider the very basic example: ...
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0answers
37 views

Simplification of a complex-valued expression with purely real components

(I'm including all the information here, as I'm not sure how much of it is necessary to solve the problem. For a tl;dr skip to the bottom) I've been working on a problem involving calculating ...
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1answer
95 views

How find solve the equation complex conjugate? [closed]

Tried solving it with every function I know but couldn't z*=z^2
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1answer
88 views

How to find all roots of a complex number [duplicate]

Finding all roots, and I know there are four f them, of this (1 - i)^(1/4) Not only real, but imaginary as well
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1answer
72 views

Rationalize complex numbers

What is the best way to rationalize complex numbers, if not both the real and imaginary part are actually rational? According to the documentation, Rationalize ...
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3answers
89 views

Plot Complex Function [duplicate]

I want to have a 3D plot for the following function: (1.6 - 0.005 I) E^(-0.5 p^2 + ( 2. I) p q + (6.5 - 11 q) q) p and q from -10 to 10 Is there any way?
2
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1answer
43 views

A question about expanding complex functions of real arguments

I have the following problem. There is such an expression as: P[x_,y_] := z[y] E^(I beta x) + Conjugate[z[y] E^(I beta x)]; The variables ...
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0answers
70 views

ComplexExpand does not treat everything as real number

ComplexExpand does not treat everything as real number?? Please read the following simple example ...
7
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3answers
427 views

How do I plot the images of oriented curves under complex transformation?

I'm working on a complex transformation sketch that I'd like to create via mathematica. I'm working with the function $$w=z^2\tag{0},$$ where its real and imaginary parts are $u=x^2-y^2$ and $v=2xy$, ...
18
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1answer
797 views

Mobius transformations revealed

Mobius Transformations Revealed is a short video that vividly illustrates the simplicity of Mobius transformations when viewed as rigid motions of the Riemann sphere. It was one of the winners in the ...
2
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1answer
121 views

Real and Imaginary parts of solutions to a complex linear ODE system

Consider a complex linear ODE system $x'=Ax$, where $$A=\left( \begin{matrix} 0&1\\ -2&-i \end{matrix}\right). $$ One can first find the eigenvalues and eigenvectors using ...
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0answers
101 views

Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form $$\left\{ \begin{align} i\frac{da_1}{dt} ...
2
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2answers
179 views

Listplot imaginary part of complex numbers

I have the following list w={{0.01,99 +0.00001414 I},{0.15,6.6370108 +0.003144129 I},{0.25,3.9515722 +0.00854493297 I},{6,0.10041 +0.28132187 I}} and I want to ...
4
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1answer
126 views

Optimizing a function containing a complex exponential

I've noticed the following significant different in performance for different formulations of the same function: ...
4
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2answers
106 views

Can't solve equation having complex coefficients

Why can't Mathematica solve $\quad\quad\frac{1-i}{\sqrt{2}}=e^{i \alpha } \tan \left(\frac{\beta }{2}\right)$ with the restrictions $\alpha \in [0, 2 \, \pi)$ and $\beta \in [0,\pi]$: ...
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3answers
107 views

Selecting a specific complex number from a list

I have a formula which is producing a large (hundreds of elements) list of complex numbers of the simple form $x+iy$. However I'm only interested in the one value which satisfies the conditions: ...
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4answers
190 views

How to extract only real solutions from the result of Solve

For Example, I have the following polynomial equations: $$ \left\{ \begin{array}{ll} \dfrac{2025 (208 x+5 (y-3446))}{52 (y+90)^2}+\dfrac{300 (8 x-21 y+1920) (y-80)}{7 (x+30)^3}+\frac{300 (80 x-21 ...
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1answer
79 views

How to solve the warning problem and obtain real roots without imaginary part?

I am trying to solve a equation with Newton's method via FindRoot, and the codes are: Define the functions: ...
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1answer
95 views

Plot sets in the complex plane [duplicate]

I just want to know if there's a way to plot sets in the complex plane. For example $$A=\{z\in \mathbb{C},z+e^{z}=0\},\\A=\{z\in \mathbb{C},\Re(z)+e^{z}\geq0\}.$$
3
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1answer
152 views

Express a complex function $f(z)$ as $u(x,y)+iv(x,y)$

How can I write a complex function $f(z)$ in the form $u(x,y)+iv(x,y)$ using Mathematica? Re and Im do not work, because they do it for complex numbers, not functions. For example, if I try ...
2
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1answer
142 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
1
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1answer
98 views

How do I solve for the real and complex parts of an equation simultaneously?

If I were to have an equation, say something similar to... (1-Sqrt[x - I y])/(1+Sqrt[x - I y]) = A + I B Where I = Sqrt[-1], is there a way for Mathematica to ...
3
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2answers
188 views

Contourplot of complex Roots

Suppose I have this equation: $$ z^2 + 3z + (x^2 + y^2) = 0 $$ I want the real and complex contour plot of $z(x,y)$. Analytically, the real/imaginary boundary is separated by condition $x^2 + y^2 ...
7
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2answers
314 views

Does FindFit support complex numbers or doesn't it?

Inspired by this previous question: Findfit doesn't give the good fit; Changing the starting values will not change the results. Consider the following complex-valued dataset. ...
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1answer
169 views

Simplifying complex expression with Mathematica

I want do get the imaginary part of Exp[I*t]/(1-Exp[I*t]) I've tried to do this Im[ComplexExpand[Exp[I*t]/(1-Exp[I*t])]] ...
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0answers
67 views

Why does this integral have a complex result

I wanted to find the normalization of distribution F2 . ...
3
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1answer
326 views

HarmonicNumber problem

I am looking for all the roots of HarmonicNumber, in the domain [-30, 1] and [0, 6000] for the real and imaginary parts, respectively, and where the parameter ...
0
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2answers
131 views

Absolute value and argument of a complex expression

I would like to find the absolute value and the argument of the expression: $ x + \sqrt { x^2 + y^2 } $ under the assumption that the absolute values of $ x $ and $ y $ are equal. I have written: ...
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1answer
99 views

Real and imaginary parts of a complex number

I would like to find the real and imaginary parts of $x + y$ in terms of polar coordinates. Here is code: ...
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3answers
112 views

Displaying the roots of a complex function using ListCurvePathPlot

I have the following algorithm: ...
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1answer
63 views

How to evaluate Floor[1/2 + Arg[z]/(2π)] with Re[z] > 0

I want to do a series expansion of an expression containing Gamma functions with specific arguments. An example is the following: ...
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1answer
110 views

how draw root locus in mathematica 9 for a special case

my closed loop transfer function is: H(s)=2exp(-q)/(1+exp(-2q)) q=sqrt((a+k*sqrt(s)+s)*s) , s=sigma+jw how can i draw root locus of H(s) as 'a' changes for ...
3
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1answer
177 views

Riemann surface for cubic root

I'm trying to generate Riemann surfaces of higher order. I read How to visualize Riemann surfaces?, and the subsequent documents. I'm able to reproduce the surface using polar representation, but I'm ...
2
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1answer
215 views

Differential Equation in Complex Plane and Parametric Plot

I would like to solve $dx/dt=\sqrt{1 + (I x)^3}$, where x is complex, for some initial condition like $1 - 5 I$ and plot the imaginary part of the solution versus the real part. (A somewhat similar ...
1
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2answers
142 views

Complex differential equation

I want to solve $dx/dt=\sqrt{(1-x^2)}$, where $x$ is complex. When I solve it by hand and analytically for some initial value and draw the imaginary part versus the real part, I obtain an ellipse, as ...
0
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1answer
120 views

Plot a real part of complex equation depending on a parameter

I would ask you to kindly provide me a way to solve this problem in mathematica way. Let the equation $z^2 + 9 -1.5 e^{- t z}=0$ where $z\in \mathbb C$ and $t\in \mathbb R^+$. In order to plot graph ...
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0answers
89 views

Complex integrals and residues

I have a question. I try to integrate this function: Integrate[Exp[I k z]*Exp[-Sqrt[k^2 - A^2]x]*Exp[-k^2*L^2/4]/Sqrt[k^2 - A^2], {k, -Infinity, -A}] But ...
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0answers
123 views

A power series expansion

Consider the function, $f(z) = z tanh(\pi z) log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ and ...
0
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0answers
60 views

Polar Plotting in Complex Plane [duplicate]

How would I plot the following functions in the polar complex plane? $$ \phi={-k\over 2\pi r}cos(\theta_0-\theta) $$ and $$ \psi={-k\over 2\pi r}sin(\theta_0-\theta) $$ Please ...
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1answer
78 views

Trouble fitting an explicitly complex model with the TransformedFit package

This is follow up from a previous question in which @Oleksandr R. suggested the use of a package he developed for splitting a model and data into real and imaginary parts to avoid a problem with ...