# 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.

1,364 questions
Filter by
Sorted by
Tagged with
100 views

### Replicating Complex Plot (branch cuts, poles, shading)

I am trying to recreate the following 2 plots: where the function being plotted is $|e^{2ipR}S_0^{\text{well}}(p)|$ where $|...|$ is the absolute value, $R=1$, and $S_0^{\text{well}}(p)$ is given as \...
• 145
45 views

### Why doesn't mathematica simplify the result of Norm in a Module calculation in this case?

I have a computation that involves the "contraction" of matrix and vector indices, see this question. I am now running into a problem of simplification when using the expression as opposed ...
• 201
1 vote
62 views

### How can I speed up symbolic integration of this highly oscillatory function?

I am trying to figure out how to speed up this symbolic integration. I have tried parallelization and numerical integration (both I am failing to implement). Here is the function: ...
43 views

1 vote
114 views

### Why doesn't Conjugate[] conjugate exponentials inside other functions?

Why does something like Conjugate[Sqrt[Exp[I x]]] give output Conjugate[Sqrt[E^(I x)]] instead of ...
1 vote
162 views

### Confused about the output of CosIntegral

I am interested in the properties of the cosine integral function, in this case the anti-derivative of Cos[Pi*x]/x, which Mathematica evaluates to ...
• 2,335
1 vote
44 views

### Trying to extract the real part of a real big and may complex number

I have this order 7 polynomium: ...
87 views

1 vote
54 views

### How does mathematica handle roots of complex numbers

When Mathematica takes $(-1)^{\frac{3}{4}}$, is it really interpreting it as $((-1)^3)^{\frac{1}{4}}$, or $((-1)^{\frac{1}{4}})^3$? These seem like they would give $e^{i \frac{3\pi}{4}}$ versus \$\...
• 1,055
160 views

### Sqrt returns complex values

I am trying to find sine from a cosine relation using the following commands: ...
• 31
1 vote
239 views

### Differential complex equations in cosmological problem

I want to solve a differential equation of second order with complex initial conditions. Despite I have wrote all the code with detail, I am still facing some problems I might want to review here. The ...
449 views

### How to verify that a certain point is a branch point for a complex function using Mathematica?

It is straightforward to verify that z=0 is a branch point for w[z]=Sqrt[z]: ...
• 2,245
44 views

### Scope of Simplifying Complex Expressions [duplicate]

Do you know what the scope of Mathematica's simplification capabilities for complex expressions is? For example, I put the heavy lifting of proving a complex inequality on Mathematica, using the ...
• 353
93 views

### Vector in the complex plane

Please tell me how I can make an animation with rotating vectors rather than rotating points. ...
• 359
150 views

### How to numerically find complex non-real roots of a function?

Using Mathematica, how can we numerically find only complexes, but not real roots, of a function? For example, if we have f:C->C, and we have roots like, R1,R2,...,Rn (real roots, without imaginary ...
• 1,536
1k views

### Make a "formula-millipede" move along arbitrary path

Math artist Chirag Dudhat specializes in simple math that does something interesting visually. He recently had a hit with a "millipede" simulation with simple complex plane formulas. Below ...
• 73.4k
72 views

...
• 21