# Questions tagged [complex]

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

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 ...
2answers
1k views

### Differentiation of an unknown function

I have to take the partial differentiation of an unknown function. For example, take the unknown function to be $g(x)$. Then it's derivative w.r.t $x$ is $g'(x)$. By default, Mathematica ...
1answer
187 views

### Need to take infinite sum of residues, is there a way to choose the order of operations for ReleaseHold?

I'm computing an infinite sum of residues. I want to do something like this: ...
1answer
61 views

### Plotting the roots of polynomials which coefficients are functions [closed]

I am working on Mathematica just for few days and I am confused to plot the roots of a polynomial which coefficients are functions. In Mathematica examples, I found some simple examples such as : <...
1answer
114 views

### Evaluating Residue at pole with different forms

I want to evaluate residues at the poles of the function $\frac{1}{z^{3/2}+r^{3/2}}$ fun = 1/ (z^(3/2) + r^(3/2)); where z ...
1answer
287 views

### How to find the pole of a equation where the residue existļ¼

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 ...
1answer
63 views

### Plotting line segments in complex plane

Recent versions of Mathematica have introduced various functions for plotting in terms of complex numbers and complex functions, including ComplexPlot, ...
2answers
210 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: ...
2answers
756 views

### Plot $\arg(z)$ in an Argand diagram and display the angle

I'd like to ask you about the way to show the $\arg(z)$ annotation about the angle. My point is to show $\frac{2\pi}{3}$ and $\frac{5\pi}{6}$ on the image. What I mean: (source: brocku.ca) Is ...
1answer
107 views

### Find roots of transcendental function in regional complex plane

I want to know how many roots does the following equation have and how to solve them all. \$f(z)=\frac{\text{sech}(35.0937 x)}{\left(e^{70.1873 x}-1.\right) x} \left((0.\, +0.0235822 i) x^2 \exp \...