Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.

learn more… | top users | synonyms

0
votes
0answers
6 views

About how Mathematica understands the branchcuts of the complex logarithm [Part 3]

One understands that for the function $log(z^2+a^2)$ Mathematica implicitly puts the branch cuts to be starting at $\pm ia$ and going up/down respectively on the imaginary axis. The phase of this ...
1
vote
0answers
32 views

Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
0
votes
0answers
56 views

Deformation of pictures [on hold]

If I get a picture, and imagine it as a complex plane, then given a function how to visualize the resulting deformed picture? Put it in this way: choose the left bottom vertex of the picture as the ...
0
votes
0answers
48 views

Always the same problem with Conjugate [duplicate]

I want to compute something like : ...
0
votes
0answers
140 views

Fastest way to create a NxNxNxN dimensional matrix

I have a function that outputs a complex number Func[x_,y_]:= blah blah; I have constructed a table of all possible values of this function. ...
0
votes
0answers
52 views

How does Mathematica understand branchcuts of the complex logarithm? [Part 2]

I observe that the answer generated by the first integration is not in any simple way related to the next two answers. (some simple jump of i 2\pi across the branchcut of the logarithm is not helping ...
9
votes
1answer
411 views

How does Mathematica understand branchcuts of the complex logarithm?

Say I have the function $f(x) = x \tanh(\pi x) \log (x^2 +a^2)$ where $a$ is some positive real number. Then it seems to be me that Mathematica when given such a ...
0
votes
0answers
32 views

Chopping pure Imaginary numbers [duplicate]

I would like to be able to Chop complex numbers and display only the non-zeroed real or imaginary part when applicable. Chop alone works just fine if the non-negligible part is only the real part. ...
1
vote
1answer
37 views

FindFit::nrlnum What am I doing wrong?

I have a model called qobs: ...
0
votes
1answer
116 views

I integrate a real function, I want a real result [closed]

I want to count some integral in Mathematica (actually, check that this integral is zero...) I arrive to an answer which has a zero real part but has some imaginary part! Why? This could be a mistake ...
0
votes
1answer
77 views

A question about using Reduce [closed]

Can someone help decipher what is the meaning of this computation that Mathematica has done? ...
0
votes
1answer
62 views

Series expansion of a complex function

How do I expand a function $f(z)$ in a particular region? For example, how would I expand $f(z)=(z^2-3z+2)^{-1}$ in the region $0<|z-1|<1.$? I believe this can be done by the binomial theorem. ...
2
votes
1answer
44 views

Determine types of input, output and internal variables in compiled functions

I am trying to speedup the computation of a longer function using Compile. For illustration consider the following short example: ...
0
votes
1answer
48 views

Simplifying complex expressions

I'm trying to work with complexes and I want Mathematica to know that all variables are real unless I explicitly assigned the variable with an I so I wrote: ...
2
votes
1answer
102 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be ...
1
vote
2answers
54 views

How to find the complex number has least and greatest modul satisfying a given condition?

Let be given the complex number $z$ satisfying the condition $|z-2+2i|=2\sqrt{2}$. I want to find the complex numbers $z$ so that their modul obtain least and greatest value. I tried. Put $z = x + y ...
3
votes
1answer
54 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
0answers
30 views

Check if a (possibly nested) list is real [duplicate]

I have a very large matrix of numbers. I want to check if all its entries are real. At the moment I am using realQ = And @@ Thread[Flatten[Im @ #] == 0] & Is ...
3
votes
1answer
201 views

How to get rid of all complex numbers and functions?

For almost esthetical reasons, I always have been fascinated by infinite sums of series and I always wonder if theyhave a closed form. A couple of days ago, I found on MSE a question related to the ...
-2
votes
2answers
74 views

Plot isn't outputting a plot [closed]

I am trying to plot the magnitude complex function (f) with respect to w. For some reason, Plot is just displaying a set of axes, with no points. Any Idea what's going on here? ...
0
votes
0answers
33 views

Plotting a complex valued function in mathematica [duplicate]

How can I plot a complex valued function like $f(z)=z^2, z=x+Iy$, in Mathematica? Can anyone help?
0
votes
1answer
95 views

Plotting discrete points on a phase plot

I'm trying to generate a phase plot of a sinusoidal voltage at discrete points using the following code: ...
0
votes
1answer
55 views

decomposing a complex equation

I have an equation such as: a*z^2 + b*(z - c)^2 == d where z is a complex variable and ...
3
votes
2answers
121 views

Complex limit gives wrong answer

I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...
1
vote
1answer
141 views

Simple way to plot a complex valued function of one real variable

How can I plot a complex valued function of one real variable, $f(t)$, as $$x=-\Re f(t),\ z=\Im\ f(t),\ y=t \space?$$ My aim is a 3-dimensional path, treating the complex valued function as if it ...
0
votes
0answers
64 views

Alternate method of conjugation using replaceall

Mathematica really struggles to simplify complex conjugates of complicated expressions - even given assumptions for every symbol in the expression being real. Often times I've found that I can ...
2
votes
1answer
76 views

Solving Complex Equation Over Reals

I want to solve the equation $\frac{abi}{a+bi}=4-2i$, where $a$ and $b$ are real numbers. I know from hand-solving the answer is $a=5$, $b=-10$. How do I get Mathematica to tell me this? I tried: ...
4
votes
1answer
152 views

Factoring a two variable polynomial in a special way

Let $$f=x^9-x^6+4x^5y+2x^3y^2-y^4$$ I would like to factorize $f$ into form: $$(y-F_1(x))\cdots(y-F_k(x))$$ over complex numbers. How can I do it with Mathematica?
2
votes
2answers
176 views

Weighted mean of complex exponential function using NIntegrate

I have defined the following functions: ...
0
votes
1answer
106 views

Bifurcation with a system of equations

I'm trying to plot a flip bifurcation diagram for a dynamical system of equations as follows: x'[t] == v[t] v'[t] == x[t] - A x[t]^3 + R*Cos[\[Omega]*t] - B v[t] ...
2
votes
2answers
127 views

Limit of a complex function

Can someone show me how to find the limit of a complex function? Example: z1 = 3 + 4*I some_function[z] = z * z1 Set-up: ...
1
vote
0answers
69 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
1
vote
1answer
139 views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
3
votes
2answers
384 views

Paths integrals in the complex plane

I can't find how to calculate path integrals of complex functions in the complex plane. For example: $$\oint_{\mid z \mid =2}\frac{1-e^z+z}{z^3 (z-1)^2}dz$$
1
vote
0answers
67 views

The number of real values assumed by combinations of complex roots of a decic

Define complex conjugate as the pair of complex numbers $a+bi,a-bi$. Assume you have 5 such pairs and they are the 10 roots $x_i$ of a 10th-deg equation with integer coefficients. In general, how many ...
1
vote
2answers
277 views

Export complex number to excel or txt file

I'm doing some calculations on complex numbers in Mathematica. I can use Export to generate a file (*.CSV or *.dat, or anything else) of complex numbers. If I want to use excel, origin or Matlab to ...
3
votes
1answer
252 views

Plotting multiple lists of complex numbers

The user #Nasser showed an elegant way to plot complex numbers: ...
3
votes
1answer
157 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 function vanishes on the line: ...
2
votes
2answers
128 views

How to plot complex values given by Solve

Update Solve[N[Table[BernoulliB[n, z], {n, 10, 10}] == 0]] ...
8
votes
2answers
1k views

How to calculate contour integrals with Mathematica?

How to calculate the integral of $\frac{1}{\sqrt{4 z^2 + 4 z + 3}}$ over the unit circle counterclockwise for each branch of the integrand?
1
vote
1answer
56 views

Substitute complex functions into complicated polynomials

Mathematica has some strange way of sorting terms. It seems that it is using a canonical sort on expressions, e.g. $\mathbb{i} \sin[x] \cos[y] \cos[z]$ is returned as $\mathbb{i} \cos[y] \cos[z] ...
2
votes
0answers
157 views

Taking real and imaginary parts of indexed functions and speeding up ComplexExpand

I am setting up a large system of ODEs and in order to use the IDA method (which is sig. faster for my system and thus attractive), I must split my equations into real and imaginary parts. I am ...
0
votes
1answer
139 views

Plot complex path (essentially a 2D path) expressed in one real parameter

Consider a complex path expressed in one real parameter, such as $$f(\alpha)=\frac{1}{e^{i \alpha} + 1},$$ which is a Möbius transformation of the unit circle. I know I can expand it all out and use ...
8
votes
0answers
421 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 ...
7
votes
2answers
679 views

How do I find line integrals?

For example, how can I calculate $$\int_{\left | z \right |=1}\frac{dz}{z}$$ I know that the answer is $2\pi i$ but how do I do it using Mathematica?
0
votes
1answer
139 views

Plotting region $f(S)$ for given complex function $f$ and $S \subseteq \mathbb{C}$ [duplicate]

I have a function $f: \mathbb{C} \rightarrow \mathbb{C}$ and I want to be able to see the effect of $f$ on any particular region of $\mathbb{C}$ e.g. what happens to the unit disk under this ...
2
votes
2answers
222 views

About Argument of complex numbers

Suppose my z = x + iy Now, if y=0, then z = x i.e it becomes a real number So, logically ...
1
vote
2answers
279 views

Draw the image of a complex region

I'm working on a complex question that asks that I determine a function that maps the complement of the region $D=\{z:|z+1|\le 1\}\cup\{z: |z-1|\le 1\}$ onto the upper half plane. That is, $f$ must ...
5
votes
3answers
214 views