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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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 ...
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2answers
651 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 ...
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1answer
709 views

Plotting multiple lists of complex numbers

The user #Nasser showed an elegant way to plot complex numbers: ...
3
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1answer
201 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: ...
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2answers
137 views

How to plot complex values given by Solve

Update Solve[N[Table[BernoulliB[n, z], {n, 10, 10}] == 0]] ...
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2answers
5k 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?
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1answer
70 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] ...
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0answers
308 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 ...
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1answer
189 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 ...
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1k 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 ...
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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?
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1answer
240 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 ...
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2answers
396 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 ...
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2answers
394 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 ...
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3answers
271 views
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2answers
648 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 ...
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2answers
423 views

How to export a table of complex numbers?

I'm having problems exporting a table of complex numbers. I have: ...
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1answer
166 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: ...
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1answer
673 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? ...
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0answers
158 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 ...
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1answer
188 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 ...
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3answers
224 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: ...
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0answers
114 views

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

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

Precision of a complex number

In an output I'm getting a number like -0.33998187034939803 + 0.I. Finding ...
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1answer
119 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 ...
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2answers
275 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 ...
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3answers
174 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 ...
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0answers
437 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 ...
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1answer
517 views

why there is a small imaginary part [closed]

I encountered a problem. I have a eigenvector eigvsI[1] ...
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0answers
411 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 ...
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3answers
232 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
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3answers
343 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: ...
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2answers
441 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 ...
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3answers
1k views

How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
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1answer
819 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 ...
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1answer
272 views

ContourPlot with parameter

I have an equation for function F[x,y]==0 which first argument x is real and another, y, ...
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1answer
153 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: ...
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2answers
236 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 ...
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6answers
1k views

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

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
502 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 ...
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2answers
314 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 ...
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2answers
314 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]]` ...
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6answers
1k 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
211 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
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2answers
605 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 ...
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1answer
385 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 ...
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1answer
2k 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
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1answer
254 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 ...
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1answer
2k 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?
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2answers
454 views

Contour plot doesn't look right

I have an implicit function expression ...