# 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.

32 views

### What does mean |sin(z)|<=1? [closed]

I already know that the magnitude of sin(z) its equal to sqrt(sin^2(x)+sinh^2(y))
51 views

### Taking the derivative of the complex conjugate/absolute value of an interpolating function

I have following code: ...
43 views

### How to find function existence border

I have a function like this f[x_, a_] = Log[-x - a]*(-x - a) + Sin[a]; this function does exist if x > a because of Log[]. a - parameters. if I plot a few graphs ...
64 views

### How to find the pole of a equation where the residue exist？

I want to calculate the residue of an equation, such as: equ = 1/((x - 2)Sqrt[x - 1]) So first I need to find the pole of the equation. My method is find the ...
49 views

### How can I plot an exponential Fourier series? [closed]

Iam triying to plot summatory of the next function: (e^(i*n*t*wo)*Sin[n*Pi/2])/(n*pi) I have no problem plotting a trigonometric fourier serie, so the only ...
33 views

### Distribute Conjugate over expression?

I have this output: Conjugate[Subscript[a, 0][x] + t^\[Beta] Subscript[a, 1][x]] I want to distribute Conjugate: ...
95 views

### Plot values of an $m\times n$ matrix on the complex plane with color varying along $m$

Let's say I have a complex valued matrix $\begin{pmatrix}1+I&2+2I&3+3I\\4+4I&5+5I&6+6I\end{pmatrix}$ represented by a list: ...
94 views

### ploting the graph of 1/z for a given value

I want to plot the graph of ${1}/{z}$ , for a specific single value of |z| (z - complex variable) . I would like something like ...
53 views

### Using DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
36 views

### How to specify in NDSolve that the sought function is holomorphic?

If I include the Cauchy-Riemann equations condition in complex form for the sought holomorphic function gf in NDSolve like this: ...
93 views

### Plot a line on the complex plane knowing one point and its orientation

I want to draw a line on the complex plane which begins at $0.4+0.1i$, and with an angle of $\frac{\pi}{4}$ with respect to the real axis. Is there a simple way to do this in Mathematica?
300 views

### Branch cuts of sqrt

I was trying to plot some complex functions with branch cuts on mathematica but I have two problems. 1) The function is with z-Sqrt[z-1]*Sqrt[z+1] with z complex. Now Mathematica says that the ...
141 views

### Why does Compile not make my function faster?

I need to speed up a large program that repeatedly calls the module below (I've not trimmed the code for this question to ensure there is enough calculation to show a speed improvement.) The obvious ...
75 views

### Simplify Re[z] in equation to more “natural” form [closed]

If you have a triangle in the complex plane with vertexes {a,b,c} (all complex numbers), the length of the altitude from A to the side BC can be computed as: ...
115 views

### How to plot list of numbers in the complex plane? [closed]

This should have a trivial solution, but how do I plot a list of (complex) numbers in the complex plane? Or, put another way, why doesn't the code below work? I get the error "... is not a list of ...
88 views

### Why can't I replace I with HoldPattern@I?

Just try this sample: I /. HoldPattern@I -> a (* I *) Why does it fail to replace I with ...
103 views

### How to plot in the complex plane? [duplicate]

I am new to Mathematica and I would like to ask how to plot in the complex plane in general. Also, as an example, how do you plot $e^{i\theta}$ in Mathematica? In physics the function $e^{i\theta}$ is ...
184 views

### How to tell Mathematica to get the real-only inverse function?

The problem I have is that Mathematica seems to play better with complex numbers so that the result of N[InverseFunction[Function[x,x^3]][-1]] is ...
78 views

### replacing complex numbers

I know: I'm going to make a poor showing, but really I can't understand this: a is an expressione whose FullForm is ...
111 views

### Imaginary part of complex number, nothing works?

I want to find the imaginary part of the complex number (a+i*b). say I have a function in the following form: ...
87 views

### Is there a simple way to get the Conjugate of a complex term, provided all information is available?

I've found a few threads addressing this, but they all seem to have pretty clunky answers, and it's hard to believe there's not a more elegant solution in Mathematica: Remove annoying Conjugate a ...
445 views

### Solving complex equations with variable exponents

How would I go about solving $(1+i)^n = (1+\sqrt{3}i)^m$ for integer $m$ and $n$? I have tried ...
65 views

### 3D-plots of Complex-parametered trig-functions returns empty plot

I first tried to plot a parametric equation as follows; ...
85 views

### Can't obtain Real results using NSolve

I am trying to find the critical properties of the Carnahan-Starling equation of state, $$p=\rho R T\frac{1+b\rho /4+(b\rho/4)^2-(b\rho/4)^3}{(1-b\rho /4)^3}-a\rho^2$$ using this system of equations, ...
116 views

### Contour plot of the imaginary portion of a function given the real part is positive

How do I plot the imaginary part of the function while its real part is positive? For example, for the below code I could have the imaginary part but I am not able to find the positive or negative ...
106 views

### Solve this equation explicitly for $\beta$

Solve this equation explicitly for $\beta$: $$T_{12}=\frac{x_{11}+x_{22}}{1+|\beta|^2}\beta$$ $x_{11}$ and $x_{22}$ are positive real numbers where $x_{11}>x_{22}$ and $T_{12}$ and $\beta$ are ...
96 views

### Simplify complex square roots

I want to simplify the following expression as follows: $$\sqrt{\left(\gamma -\kappa _2\right){}^2-16 G_2^2}=i\sqrt{-\left(\gamma -\kappa _2\right){}^2+16 G_2^2}$$ I am trying ...
59 views

### Unable to simplify the real part of a complex expression

Simplifying this expression shouldn't be hard. I tried adding assumptions asserting that all involved variables are real, but still the Re expression remains ...
70 views

### Complex polynomial variable transformation

I have two real polynomials that depend in variables (xi1, xi2) and parameters (eps, e2). I apply the following complexification:...
57 views

### Why doesn't a real variable's conjugate evaluate to itself?

I have this code (it's just a snippet to exemplify my issue): Assuming[Element[a, Reals],Conjugate[a]] Which results in the output: ...
94 views

### Fitting real and imaginary parts of a function

I have an analytic form of a function G[w_] = -I*z0*w/(1 + I*z0*w*a) I know this function can be obtained (up to some overall normalization) from solving a ...
126 views

### How do I calculate this integral along a complex line (not a contour) in mathematica?

Given the function: $$f(z) = \frac{\pi ^2 \cot(\pi \sqrt z) \cot(\pi \sqrt {z-a})}{4\sqrt{z^2 - az}}$$ Where a is a positive constant and: $$z = \frac{i}{b} + t$$ $$t>a$$ Where b is also a ...
91 views

### Expression containing $\tt{I}$ is real — how can I show this is so in my notebook?

When I solve this equation (for ϕ): -16 y - (1 + 2 ϕ)^2 (-1 + 6 ϕ) == 0 Two solutions have imaginary parts in the symbolic ...
90 views

### Display the list of complex roots returned by Solve in their polar form [duplicate]

If I input: Solve[z^4 == 2 (Cos[2 Pi/3] + I Sin[2 Pi/3])] Mathematica returns: ...
67 views

### Using NSolve for Elliptic Equations over Fundamental Parallelogram in Complex Plane [closed]

I'm considering solving elliptic functions over a fundamental domain of the torus with half-periods $\omega_{1}=\pi/2$ and $\omega_{2} = \pi \tau /2$, where $\tau$ is the modular parameter of the ...
64 views

### Plotting an expression with a complex-valued exponential [duplicate]

Given the wave function $\Psi\left ( x,t \right ) = \psi\left ( x \right )T\left ( t \right )$ with the spatial component of the wavefunction $\psi(x) = \psi_{0}e^{-ikx}$, I tried ...
123 views

### How can I draw a hyperbola of a complex form

How can I use Mathematica to draw locus of point in complex plane given by $||z-i|-|z+i||=1.$ I have tried few codes, but not succeed.
98 views

### Problem with complex conjugation of series data in mathematica 10

ComplexExpand in Mathematica 10 doesn't work with series data: Taylor = Series[Exp[I x], {x, 0, 4}]; ComplexExpand[Taylor\[Conjugate]] gives 1+I x-x^2/2-(I x^...
89 views

### Integrating sinc function over discontinuity

I would like to analytically integrate the sinc function. First of all, if I just perform the integration the following way, everything is as expected: ...
89 views

### FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
70 views

### Finding consecutive residues of large expression?

I have given a large expression expr (has LeafCount of 2772, you can find it in this file or ...