# Tagged Questions

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

1answer
49 views

### Overloading conjugate operator for a particular function

I trying to modify the behaviour of the built-in Conjugate[] operator on a particular function I have defined, to take into account that some of its variables are real. ...
3answers
86 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 ...
0answers
77 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 ...
1answer
92 views

### why there is a small imaginary part [closed]

I encountered a problem. I have a eigenvector eigvsI[1] ...
0answers
76 views

### Solve equations real and imaginary part separately

For my system of equations, the procedure described in Solving complex equations of using Reduce works no more. How can I separate the real and imaginary part of ...
2answers
50 views

### Conjugate and simplify

I want to get a cosine from taking the real part of a complex exponential: $cos(x) = Re(exp(i x))$. What I do in Mathematica is ...
3answers
125 views

### How to extract phase angle from sinusoid

I'm doing some electric circuit calcualtions and I'm trying to get the phasor representation of some arbitrary function of Sin or Cos. Could be complex like: ...
0answers
70 views

### ComplexExpand absolute squared

ComplexExpand[Abs[a + b I]] Gives $\sqrt{a^2 + b^2 }$ ComplexExpand[Abs[a + b I]^2] On the other hand gives Abs[a ...
2answers
74 views

### How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
1answer
97 views

### Plotting a complex function [duplicate]

What does it mean if this message appears: {Im[(1-E^Times[<<3>>] f)/(1-Power[<<2>>] f)]-0,Im[(1-E^Times[<<3>>] f)/(1-Power[<<2>>] f)]-0} must be a list of equalities or ...
1answer
130 views

### ContourPlot with parameter

I have an equation for function F[x,y]==0 which first argument x is real and another, y, ...
1answer
85 views

### Simplifying Complex Numbers that contain physical units

I am trying to evaluate the following: Simplify[Meter Nano Re[(a + I b)/(Meter Nano)], Assumptions -> Element[{a, b}, Reals]] However, Mathematica returns: ...
2answers
139 views

### Convergence and value of a complex power series

I've done a little math and I got the following power series expansion of $\log z$ about $z_0=-2+i$. $$\log z=\log(-2+i)+\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n(-2+i)^n}[z-(-2+i)]^n$$ I've shown that ...
5answers
409 views

### Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do? [closed]

The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration. ...
0answers
66 views

### Choosing the appropriate solution for the square root [closed]

My problem is the following: given the function myfunc[x_, a_]:= (a^3 - (a^2)^(3/2))/(x) the limit as x goes to 0 should be well defined and = 0. However, ...
1answer
255 views

### How do I put an image on the complex plane?

I watched this video and became interested in transforming an image. But I have no good idea on how to embed an image in the complex plane using Mathematica. I have a method that seems to work, but ...
2answers
211 views

### Inconsistent results from equivalent integrals

Why is Mathematica returning different values for these two integrals: I am just being introduced to complex integration, so it's possible that I have a misunderstanding of how this works, but in ...
2answers
157 views

### What is the value Re[Sqrt[1+I*2*x]]?

When I try to evaluate Re[Sqrt[z]], for some values of Mathematica fails to evaluate it. For example, Re[Sqrt[2 + I*x]]` ...
6answers
339 views

### Image of first quadrant under $f(z)=(z+i)/(z-i)$

I'm able to plot the region where Im[z] > 0 and Re[z] > 0: ...
3answers
117 views

### Wrapper for inexact numeric complex numbers that maintains polar form

Related question: How can I convert a complex number a+b I to the exponent form A Exp(I phi)? Mathematica insists on displaying complex number in form a+I b when ...
2answers
159 views

### What can I do to eliminate the error FindFit::nrjnum:?

I am testing the "Power Law with finite-time singularity" hypothesis for world population growth for a project. The data I'm using (same behaviour should also be exhibited by the stock market, thats ...
1answer
130 views

### Stop Mathematica from giving imaginary solutions

I have the following equation: $$D=\frac{1}{64} \pi A ^3 B \sin \left(C\right)-\frac{1}{2} \pi A B \sin \left(C\right)$$ which I want to solve for $A$. The equation is cubic in $A$ so this should ...
1answer
123 views

### How can I get the solution of complicated implicit function?

The question is what is the method to solve the implicit function has real and imaginary number. For example, The function is F(x,y)=(-I*x + 2*y^2)^2 + x^2 - 4*y^4*Sqrt[1 - I*x/(y^2)]. Although I ...
1answer
116 views

### Compiling Error functions of complex values

According to List of compilable functions Erf and Erfc are compilable functions. However, I want to make a compiled version of ...
1answer
418 views

### Complex line integral

Can someone recommend an online article or introductory tutorial that will show me how to do real and complex line integrals using Mathematica?
2answers
285 views

### Contour plot doesn't look right

I have an implicit function expression ...
0answers
41 views

### Contour integration [duplicate]

Possible Duplicate: Symbolic integration in the complex plane Does mathematica do Contour integration ? like this one : $\displaystyle \oint_{\gamma} f(z)\ \mathrm{d}z$ if yes, how ...
2answers
169 views

### Adding multiple Complex Numbers in Euler form

Say I have a series of $n$ complex numbers of the form $A_k e^{(I \ \theta_k x)}$ where $A_k$ is a real number and so is $\theta_k$ and $k$ runs from $1$ to $n$. $x$ is an algebraic symbol. ...
3answers
436 views

### Solving cubic equation for real roots

I'm looking to solve the following cubic equation for x: $\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this ...
1answer
327 views

### Forcing FindRoot to return only real solutions

FindRoot documentation reports that if the Equation and the initial point are reals, the solutions are searched in the real domain. However, in the following case I ...
2answers
166 views

### How to eliminate the zero real part of a purely imaginary number?

In Mathematica 9, a purely imaginary number, e.g. 0.9 I, will display as 0. + 0.9i in the output form. How can I eliminate the ...
1answer
101 views

### Manipulate[]'ing complex roots of an equation using a 2D slider [closed]

I want to make a demonstration of how the complex roots of a polynomial change when I alter the coefficients. Here is my attempt: ...
3answers
169 views

### Show does not combine the plots

i've the following problem: because it's not possible to plot complex numbers (or is it?) i created my own "function": ...
1answer
107 views

### Why am I not getting Indeterminate for f[1] when f[x_] = (x - 1)/(x - 1)? [closed]

In Mathematica 9 If I write: f[x_] = (x - 1)/(x - 1) I get 1 And if then I write: ...
3answers
329 views

### How can I convert a complex number a+b I to the exponent form A Exp(I phi)?

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 ...
2answers
438 views

### Linear equation with complex numbers

I have to solve an equation of the type $$a z+b \overline{z}=c$$ with $a,b,c\in\mathbb{C}$. My approach is to set $F(z)=a z+b \overline{z}-c$ transform $z$ to $x+i y$ and then get a real linear ...
1answer
304 views

### Bifurcation diagrams for multiple equation systems

I am interested in constructing a bifurcation diagram for some of my parameters (especially for β and γ) in the dynamical system given in the code below. I want to see how parameter changes affect the ...
4answers
1k views

### Plotting 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 ...
1answer
104 views

### Exporting/Importing a Table of complex numbers

I'm generating a long table of list of the form: PN={{1,2,1+i},{3.5,2.6,2}...},{...},... Using: Export["PN.dat", PN, "Table"] ...
0answers
100 views

### Why does Mathematica choose branches as it does in this situation?

Consider these integrals: ...
2answers
224 views

### Moving the location of the branch cut in Mathematica

According to the documentation, Mathematica chooses the branch cut for $\log(z)$ to lie along the negative real axis. It it possible to change this so that it lies along the positive axis or elsewhere ...
0answers
151 views

### Function approaching incorrect limit in mathematica [closed]

I am interested in the complex function $f(z)=\frac{1}{a}\log\left[2\sinh(a\sqrt{z})\right]$. where $a > 0$ is a real parameter. Clearly for large $a$ this approaches $f(z) \to \sqrt{z}$. But ...
2answers
303 views

### Eigensystem, Eigenvalue doesn't output nonreal eigenvalues

Basically I have a matrix and when I used either Eigenvalue or Eigensystem, it doesn't output nonreal eigenvalues, instead it ...
1answer
148 views

### Testing for primality in quadratic rings?

Testing for primality in $\mathbb{Z}[\sqrt{-1}]$ in Mathematica is easy: PrimeQ[n, GaussianIntegers -> True] But how can I test for primality in, say, ...
1answer
233 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 ...
0answers
277 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 $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
1answer
326 views

### Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
1answer
253 views

### Finding residues of multi-dimensional complex functions

Say I have a function $f$ of $n$ complex variables, $\{ z_i \}_{i=1}^{i=Nc}$. And then I want to contour integrate the expression such that for each $z_i$ its an integration on an unit circle about ...
1answer
309 views

### Is Abs[z]^2 a bad way to calculate the square modulus of z?

For a numerical quantity z, Abs[z] returns the square root of the sum of the squares of the real and imaginary parts of ...
2answers
308 views

### Is there a way to solve the Apollonius Circle problem in Mathematica?

Assuming x, a, and b are complex numbers, is there a way to reduce the equation Abs[x - a] == k Abs[x - b] to something like ...
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