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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2
votes
2answers
57 views

Reading from a file: complex number with small imaginary part

I'm trying to read a matrix from the next file: 1+1e-18i 24 42 23.43e-23i using u=Import["file.dat","Table"]; and then find, ...
1
vote
0answers
24 views

Evaluating Real and Imaginary parts in a dispersion equation via ContourPlot

I am attempting to solve a dispersion equation which has real and imaginary components. I do this by using ContourPlot with Evaluate; however the solution only gives Real values. I got around it by ...
2
votes
0answers
395 views

Simple contour integral with a parameter gone wrong

Bug introduced in 7.0 and fixed in 7.0.1 I run into the following problem, I tried to evaluate a very simple integral: ...
16
votes
0answers
2k views

How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
0
votes
0answers
11 views

Physical interpretation of residues [migrated]

What is physical interpretation of residues of poles (of any order) of a complex function? Poles represents the points where a complex function cease to be analytic and residues are calculated to ...
3
votes
1answer
573 views

How to make the imaginary part of a +0. I zero globally?

Values like a +0. I are really annoying. Answers from How to reduce expressions with complex coefficients in the form of a+0.*I? Is there a way to globally set when to treat a very small number as ...
12
votes
5answers
4k views

Plotting complex numbers as an Argand Diagram

I have the function: $F(\omega) = \frac{5\; - \;i\;\omega}{5^2\; +\; \omega^2}$ When $\omega$ has the values : $\{ -7, -2,\; 0,\; 2,\; 7\}$ How would I plot the Argand diagram in Mathematica? Or ...
0
votes
0answers
35 views

Graphing imaginary numbers [duplicate]

I'm solving [Sum(i=1..p) x^i] = 100. The max value of 25 is arbitrary. I would like to see how the solutions look in 2-dimensional space. How do I view an imaginary number on a Cartesian coordinate ...
3
votes
1answer
88 views

Complex LogIntegral error

Going through Derbyshire's Prime Obsession & trying to take LogIntegral of 20^ZetaZero[1] & comes up with a value of ...
0
votes
2answers
37 views

Equality of expressions containing complex numbers [closed]

I am using Mathematica to test the equivalence of symbolic expressions. I run into what appears to be a bug when I test the equivalence of expressions involving an imaginary number taken to a complex ...
0
votes
2answers
74 views

Summing complex numbers

Maybe it is a very stupid question but I am having trouble with summing complex numbers in Mathematica. I have q = l1 E^(2 π I t1) + l2 E^(2 π I t2) where ...
3
votes
2answers
117 views

How to declare a function as real in order to get rid of Conjugate in front of the expressions?

I have a complicated complex function containing some other ones that are real, f=f(A,B,C,...) ,where A=A(r) and it is real, for ...
0
votes
0answers
62 views

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

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: ...
0
votes
0answers
39 views

Please explain this unexpected code snippet behavior [duplicate]

Consider a function that maps a complex function z->f(z) to it's multivariable counterpart (x,y)->f(x,y) ...
5
votes
1answer
69 views

How to calculate residues using different branches of the logarithm

My goal is to be able to compute the residues of something like $z^{\alpha} R(z)$ where $0 < \alpha < 1$, $R(z)$ is rational, and the exponential can be chosen with any branch. I found a way to ...
3
votes
1answer
169 views

Factoring the imaginary unit

Suppose you have this: Collect[2 u + I + 2 + I,I] It gives the same. Is it possible to factor I in elegant way (not ...
2
votes
2answers
114 views

Plotting a set of points given by a complex expression [closed]

A have the set consisting of the complex numbers $1+3r \cosθ−ir \sinθ$, where $r∈[0,1]$ and $θ$ may vary between $0$ and $2π$. This is my first encounter with Mathematica, and am having difficulty ...
3
votes
0answers
50 views

Why does FreeQ seem not to work with complex numbers?

I guess I do not understand how Mathematica evaluates this simple expression inside FreeQ ...
5
votes
2answers
246 views

When does the real part of Zeta vanish on the critical line?

This seems to be a quite a simple problem but I cannot make it work. I am trying to find all values within a given range for which the real part of the Zeta ...
14
votes
3answers
2k views

How can I convert a complex number into an exponent form

When I have an expression such as (1/4 + I/4) ((1 - 2 I) x + Sqrt[3] y) it is hard to get an intuition of the number. So I want to convert it to the complex ...
2
votes
1answer
131 views
0
votes
3answers
79 views

Plotting complex function

(9 Tanh[x]^8 (1 - 2 Tanh[x]^2)^2 (1 - Tanh[x]^2))/(1 + 3 I Sqrt[2/13])^2 How can I plot the function with the range of x {-10,10}?
2
votes
1answer
68 views

Wrong result after Simplify of a complex variable with assumptions satisfying an inequality

Using Mathematica 10,Simplify[a\[Conjugate], Assumptions -> {(a + a\[Conjugate]) > 0}] returns a, i.e. treats ...
3
votes
1answer
457 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 ...
37
votes
2answers
1k views

Möbius transformations revealed

Möbius Transformations Revealed is a short video that vividly illustrates the simplicity of Möbius transformations when viewed as rigid motions of the Riemann sphere. It was one of the winners in the ...
17
votes
1answer
687 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitely. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
8
votes
1answer
949 views

Stereographic Projection

Say I want to represent points of the complex plane in the sphere $\Bbb S^2$ using stereographic projection. That is, the Riemann sphere: Specifically, it would be nice to be able to: Given the ...
1
vote
2answers
163 views

Complex numbers from two arrays with Real and Imaginary parts

I have two arrays, containing the real and imaginary parts of a list of complex numbers. Re = {{Re_number1},{Re_number2},...} Im = {Im_number1},{Im_number2},...} ...
3
votes
0answers
93 views

Discrepancy in the series expansion of $\log(z/(z-1))$ in Mathematica 5

When I calculate the series expansion of $\log\frac{z}{z-1}$ around $0$ in Mathematica 5.2, I obtain: ...
0
votes
1answer
53 views

Plotting the image of a curve under a complex polynomial using Mathematica

I would be able to plot the image of a curve (say the circle with radius $1$ centered at $1+i$) under a complex polynomial (say $p(z)=z^2$) using Mathematica. I know how to find the level curves of ...
0
votes
1answer
76 views
0
votes
1answer
121 views

ComplexExpand does not treat everything as real number [closed]

ComplexExpand does not treat everything as real number?? Please read the following simple example ...
0
votes
1answer
43 views

Compute and Plot the element of a complex sequence

I'm new tho mathematica. I have a complex sequence ${z_n}$ with $z_0:=c$ $z_{n+1}=(z_n)^2+c$ for all $n\in N$ where c is some complex number, I need to plot the first 20 terms of this sequence ...
0
votes
1answer
59 views

Conjugate of I \[Phi] [closed]

I have a bigger expression of which I have to take the conjugate. But this is in itself perplexing. When I write ComplexExpand[Conjugate[I\[Phi]]] I just get ...
5
votes
1answer
172 views

How to plot the solution of a Partial Differential Equation?

My attempt. I need to solve numerically the Complex Ginzburg-Laudau Equation (CGLE): $$ \frac{\partial A}{\partial t}=\epsilon A-(1+i\beta)|A|^2A+(1+i\alpha)\nabla^2A $$ I'm using a uniform initial ...
5
votes
0answers
139 views

Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
1
vote
0answers
88 views

Real part of a sum

I would like to take the real part of the following expression: Sum[(a[i] + I b[i]) r^i/(r^2 + z^2)^i, {i, 0, 2 n}] where all of ...
1
vote
1answer
251 views

How to plot the graph of the equation F[x,y]=0 if y is real number, x is complex? [closed]

I have an equation F(x,y;a,b,c,...)=0, where x and y are variables, a,b,c,... - parameters. y is a real number, x - complex. For every given y I need to solve this equation, i.e. to find Im(x) and ...
1
vote
3answers
211 views

finding an argument of a complex number

What is the simplest way to find the argument of the following function? ((1 - E^((I π (1 - α))/(β - α)) z)/(1 - E^(-((I π (1 - α))/(β - α))) z)) as I tried the ...
1
vote
4answers
2k views

How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
0
votes
1answer
90 views

How to obtain Laurent series coefficients of an (almost) arbitrary function?

I have observed that Series in Mathematica assumes that the given function is smooth in the point around which one wants to perform series expansion. For instance: ...
0
votes
1answer
51 views

How to get the modulus of following complex number

I want to get the modulus of following (1+(x+I*y)/2+(x+I*y)^2/12)/(1-(x+I*y)/2+(x+I*y)^2/12) I use ...
36
votes
6answers
6k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
19
votes
4answers
13k views

Plotting Complex Quantity Functions

Trying to plot with complex quantities seems not to work properly in what I want to accomplish. I would like to know if there is a general rule/way of plotting when you have complex counterparts in ...
9
votes
3answers
123 views

Pattern matching with Complex. Feature or a bug?

fixed in 10.1 (windows) I have run into some strange behavior while doing some pattern matching. First, this works as expected: ...
8
votes
2answers
194 views

Strange behavior of Limit in Mathematica 9 and 10 (bug?)

fixed in 10.1 Consider a complex logarithm where the branch cut is defined along the negative axis. Then for $r$ and $\eta$ real and positive we can write $ \lim_{\eta \to 0} \log(-r+ i \eta) = ...
10
votes
1answer
397 views

Symbolic Integration along contour: branch cut problem?

Context Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as ...
1
vote
1answer
128 views

Working with derivative of conjugate of a complex number

I have a complex function, lets say $g(x)$. I want to take its and its conjugate's derivative. I need the solution of derivative which must be symbolically and computationally efficient. Lets take an ...
1
vote
1answer
98 views

Polar color coding for complex function plots?

Having browsed this Q on plotting complex functions and the Zeta page, I don't see anything as nice as this plot from Matilde Marcolli's slides "Geometry and physics of numbers". Looks like ...
5
votes
3answers
611 views

Complex conjugate

How do I complex conjugate a vector? ...