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
1answer
72 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
votes
2answers
219 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. ...
1
vote
1answer
55 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])]] ...
0
votes
0answers
41 views

Why does this integral have a complex result

I wanted to find the normalization of distribution F2 . ...
3
votes
1answer
267 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
votes
2answers
77 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: ...
1
vote
1answer
62 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: ...
0
votes
3answers
94 views

Displaying the roots of a complex function using ListCurvePathPlot

I have the following algorithm: ...
0
votes
1answer
49 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: ...
-2
votes
1answer
69 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
votes
1answer
110 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
votes
1answer
121 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
vote
2answers
121 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
votes
1answer
84 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 ...
0
votes
0answers
47 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 ...
0
votes
0answers
75 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
votes
0answers
52 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 ...
0
votes
1answer
69 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 ...
0
votes
1answer
57 views

Can't Plot Fourier Series [closed]

I have been trying to plot fourier series but the plot is allways empty. I guess there is something wrong in my code but i dont know exactly what is it. Looking here for some previous ...
-2
votes
1answer
144 views

How to solve a non-linear equation?

I am trying to solve the following non-linear equation: $\frac{i e^{-x^2} \sqrt{\pi } x}{K^2}+\left(-0.131251-0.0379031 x^2-0.0151154 x^4-0.0100462 x^6+0.5 \left(0.00273859 +0.0400003 K^2\right) ...
0
votes
0answers
67 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
43 views

Conjugate of InterpolatingFunction?

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

Always the same problem with Conjugate [duplicate]

I want to compute something like : ...
0
votes
0answers
430 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
67 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
514 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
36 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
68 views

FindFit::nrlnum What am I doing wrong?

I have a model called qobs: ...
0
votes
1answer
132 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
82 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
84 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
66 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
51 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
114 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
96 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
63 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
31 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
235 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
81 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
36 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
119 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
61 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
134 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
246 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
90 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
80 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
181 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
189 views

Weighted mean of complex exponential function using NIntegrate

I have defined the following functions: ...
0
votes
1answer
152 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] ...