# 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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### How to convert DifferenceRoot into a special function?

Clear["Global`*"]; f[z_] := z^(2 m) /(1+z)^m res = SeriesCoefficient[f[z], {z, -1, -1}, Assumptions -> Element[m, PositiveIntegers]] The result ...
90 views

### Missing plot for double derivative with log

I want to plot the given code of double derivate with log function. My derivative is a function of delta P. But when I run the code, I never see the plot. ...
54 views

### Plotting diagram of complex equation [closed]

I have this equation: q1[t_] := -I*γ*Sin[θ] + ((γ*Cos[θ])/n^2)*(I*ξ[t]*y+z*α[t]) and the main code is the following with the definition of each parameters: ...
54 views

### Taking the Unit Disk as a Domain for ComplexRegionPlot

I am very new to Mathematica and overall not very good with programming. I want to plot the region $|(\frac{z}{f(z)}f'(z))^{1+q}-1|<1$ where $z$ is taken from the unit disk and $0<q<1$. In ...
65 views

### Successive multiplications using Mathematica tools

Successive rotations on the unit circle Given an arbitrary starting point $z$ on the unit circle in the complex plane, the goal is to compute a cycle of rotations by $\pi$/2 with successive ...
120 views

### Complex integral with branch cuts

I am struggling with a complex double integral with multiple branch cuts. Even the single variable complex integral I find quite complicated due to the branch cut and the special functions involved in....
49 views

### How to simplify the following expression of a matrix with complex conjugation?

Consider the following matrix: ...
1 vote
97 views

### Mathematica fails to correctly recognize Hermitian matrix

I have a Hermitian matrix, but Mathematica gives 'False' when I try with HermitianMatrixQ. ...
1 vote
105 views

### How to transform a complex quotient involving absolute values and conjugates into the rectangular form?

I am relatively new to Mathematica and I am still trying to figure out all the commands. I have these three complex numbers: And I wish to calculate the following quotient and write it in the a+bi ...
52 views

### How to correctly represent any Power function and How to draw the image of Power function correctly? [duplicate]

Why is the result of solving this inequality incomplete?Is it a BUG in the software? According to cvgmt's answer to the previous question, I review the function images of Power function again, and ...
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### Why is the result of solving this inequality incomplete?Is it a BUG in the software? [closed]

Solve this inequality In:= Reduce[x^2 > x^(1/3), x, Reals] Out= x > 1 Missing a solution as x<0 There was ...
156 views

### Result of numerical computation representing a real physical quantity still contains a small imaginary components [closed]

I have been grappling with a physics calculation pertaining to thin film optics. I have been endeavouring to use transfer matrix calculations to determine optical reflectance. Attached below is the ...
59 views

### Computing the continuous eigenvalues of a family of matrices

I want to compute the eigenvalues of a family of $2 \times 2$ unitary matrices $M: [0, 2 \pi] \to U(2), k \mapsto M(k)$, which is given by \begin{align*} M(k) = \frac{1}{2} \, \begin{pmatrix} ...
200 views

### Simple sum runs endlessly

I tried evaluating Sum[-(1/(2 X (-X+vF (I+y) (I T+n β))^3)),{n,-∞,∞},GenerateConditions->False] which did not terminate. Whereas the modified sum ...
199 views

1 vote