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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3
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1answer
537 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 ...
0
votes
1answer
141 views
0
votes
1answer
242 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: ...
3
votes
1answer
136 views

Decomposing a complex numbers equation into its real and imaginary part

I have an equation such as: a*z^2 + b*(z - c)^2 == d where z is a complex variable and ...
3
votes
2answers
179 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: ...
2
votes
1answer
2k 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
172 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
120 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
268 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
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2answers
279 views

Weighted mean of complex exponential function using NIntegrate

I have defined the following functions: ...
0
votes
1answer
267 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
255 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: ...
2
votes
0answers
111 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: ...
4
votes
2answers
767 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: ...
6
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2answers
2k 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
72 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
760 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
792 views

Plotting multiple lists of complex numbers

The user #Nasser showed an elegant way to plot complex numbers: ...
5
votes
2answers
243 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 ...
2
votes
2answers
138 views

How to plot complex values given by Solve

Update Solve[N[Table[BernoulliB[n, z], {n, 10, 10}] == 0]] ...
19
votes
2answers
6k 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
74 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] ...
3
votes
0answers
348 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
203 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 ...
15
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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 ...
8
votes
2answers
2k 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
280 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
449 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
430 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
291 views
1
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2answers
774 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
478 views

How to export a table of complex numbers?

I'm having problems exporting a table of complex numbers. I have: ...
2
votes
1answer
171 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: ...
2
votes
1answer
796 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
180 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
vote
1answer
220 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 ...
3
votes
3answers
256 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
115 views

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

after plotting this function: ...
2
votes
1answer
125 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
votes
2answers
305 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
vote
3answers
204 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
votes
0answers
506 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 ...
2
votes
1answer
666 views

why there is a small imaginary part [closed]

I encountered a problem. I have a eigenvector eigvsI[1] ...
0
votes
0answers
452 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
votes
3answers
248 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
369 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: ...
4
votes
2answers
489 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 ...
8
votes
1answer
925 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
4answers
2k views

How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
1
vote
1answer
916 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 ...