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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1
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2answers
383 views

Contour plot of complex function: problem in choosing argument

I have a complex function F[x,y], and now I want to plot the contour F[x,y] = 0. What can I do in order to have the contour plot vs Re[x] and y (That is, I want to treat y a real variable and x a ...
2
votes
2answers
199 views

How to export a table of complex numbers?

I'm having problems exporting a table of complex numbers. I have: ...
2
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1answer
151 views

A question about derivatives (cubics)

Given an equation: f(z) = a (x + I y)^3 + b (x + I y)^2 + c (x + i y) + d Which can be re-written as: ...
1
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1answer
316 views

How can I plot a hyperbola from its complex representation?

How can I plot the hyperbola represented by the following complex equation: $$\left|z-a\right|-\left|z-b\right|=2t\tag{1}$$ Should I convert (1) into the following form? ...
0
votes
0answers
141 views

Assigning numerical values to constants results in complex coefficients in Equations of Motion

I am using Mathematica to get the Equations of Motion (EOM) for a mechanical system (using Lagrangian Mechanics). While I get the EOM in symbolic form, on introducing the following code for assigning ...
1
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1answer
105 views

Using Collect to gather explicitly imaginary terms

Collect[Expand[(x + I y)^6], I] yields x^6 + 6 I x^5 y - 15 x^4 y^2 - 20 I x^3 y^3 + 15 x^2 y^4 + 6 I x y^5 - y^6 How can I ...
1
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3answers
143 views

Conjugating symbolic expression

I am trying to conjugate a symbolic expression, and I have explicitly stated the real terms. However, I simply can't get it to work: ...
0
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0answers
112 views

How to add something like a shadow to my resulting figure? [duplicate]

after plotting this function: ...
0
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0answers
105 views

Precision of a complex number

In an output I'm getting a number like -0.33998187034939803 + 0.I. Finding ...
2
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1answer
107 views

from complex function to a series

How can I express this complex function as a series? Log[ (1 - E^((I Pi (1 - a))/(b - a)) z)/ (1 - E^(-((I Pi (1 - a))/(b - a))) z) ] Where ...
3
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2answers
181 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 ...
1
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3answers
108 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 ...
2
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0answers
219 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 ...
1
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1answer
227 views

why there is a small imaginary part [closed]

I encountered a problem. I have a eigenvector eigvsI[1] ...
0
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0answers
299 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 ...
0
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3answers
142 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 ...
3
votes
3answers
243 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: ...
1
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0answers
171 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 ...
1
vote
2answers
719 views

How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
1
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1answer
555 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 ...
0
votes
1answer
205 views

ContourPlot with parameter

I have an equation for function F[x,y]==0 which first argument x is real and another, y, ...
0
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1answer
129 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: ...
4
votes
2answers
195 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 ...
3
votes
5answers
893 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. ...
5
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1answer
403 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 ...
15
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2answers
285 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 ...
8
votes
2answers
265 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]]` ...
5
votes
6answers
816 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: ...
7
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3answers
167 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 ...
4
votes
2answers
402 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 ...
1
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1answer
262 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 ...
0
votes
1answer
770 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 ...
6
votes
1answer
183 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 ...
0
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1answer
1k 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?
5
votes
2answers
416 views

Contour plot doesn't look right

I have an implicit function expression ...
1
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2answers
269 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. ...
1
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2answers
718 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 ...
2
votes
1answer
1k 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 ...
6
votes
2answers
266 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 ...
0
votes
1answer
151 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: ...
3
votes
2answers
242 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": ...
0
votes
1answer
118 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: ...
10
votes
3answers
980 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 ...
3
votes
2answers
852 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 ...
6
votes
1answer
1k 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 ...
6
votes
4answers
2k 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 ...
3
votes
1answer
281 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"] ...
11
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0answers
157 views

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

Consider these integrals: ...
8
votes
4answers
496 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 ...
2
votes
2answers
377 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 ...