# 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.

928 questions
Filter by
Sorted by
Tagged with
4k 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: ...
554 views

### Complex result for Real vectors in VectorAngle

I was expecting a real angle using VectorAngle when passing real valued vectors, but I obtained a complex angle: ...
8k 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?
792 views

### How to use Mathematica to do a complex integrate with poles in real axis?

I want to use Mathematica to compute the following complex integral: Integrate[Exp[I z ] 1/z, {z, -Infinity, Infinity}] Mathematica reports that it does not ...
4k views

### Laurent series expansion

Can someone share how to find the Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at $0$ on the annulus $1<|z|<2$?
3k views

### Is it possible to set a variable as a positive one in the whole notebook?

I'm having issues during integration due to the fact that Mathematica doesn't know if an undefined variable is positive or not (it gives me complexes which bothers me in the end). For example I do ...
552 views

### Complex continuation of an interpolated function

Context I have a complicated real function defined implicitly by a series of imbricated numerical integration. I need to make a continuation of this function for a complex variable which is easily ...
225 views

### Multiplying two complex SparseArray objects, yielding empty SparseArray crashes kernel

Problem: When I multiply together two sparse matrices that should give back the 0 matrix, where at least one element among the two is complex and at least one is not an exact number, the kernel ...
507 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]]` <...
2k 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 ...
705 views

### Visualizing the primes with the Riemann Zeta function

I am trying to plot the identity seen here, namely that if we define: $$\psi _{0}(x)={\frac 12}\left(\sum _{{n\leq x}}\Lambda (n)+\sum _{{n<x}}\Lambda (n)\right)$$ Then, it equal to the following,...
174 views

### Problem with Identifying Complex Components

I am trying to isolate out the real and complex terms in a fairly large expression. During the process, I have made several assumptions that last throughout the entire process. ...
441 views

### NDSolve for complex BVPs and FindRoot

NDSolve works for complex valued ODE initial value problems (IVP). However, for a simple boundary value problem (BVP) with complex coefficients it fails: ...
175 views

### Pattern matching with Complex. Feature or a bug?

fixed in 10.1 (windows) I have run into some strange behavior while doing some pattern matching. First, this works as expected: ...
319 views

### Why ArcTan[1, 0. I ] yields -1.5708+0. I?

Bug introduced in 5.2 or earlier and persisting through 12.0.0 Why ArcTan[1, 0. I ] yields -1.5708+0. I ? The result should ...
373 views

### Contour integration, residues and precision of the poles

Task I am trying to evaluate the contour integral of some functions. To have a concrete example, let's use $$f(z,s) = \frac{1+(4+2s)\, z}{z - \left( 9 + 35s + 24s^2 + 4s^3 \right) z^2 + 8z^3}$$ <...
374 views

### Integrate and NIntegrate disagreeing over branch cut of Sqrt?

Bug introduced after 8.0.4 and before 9.0.1, and fixed in 11.1.0. In Mathematica 10.2 I'm trying to integrate this piecewise continuous function, but Integrate and ...
2k views

### RootSearch for complex or multiple equations

First the background. I'm trying to solve for the roots of a rather messy complex equation. This is not the exact equation, but it's a decent (simpler) stand in: ...
2k views

368 views

### Why does N[Re@f] give complex result?

Consider this code: ...
545 views

### Getting Arg[z] to go from $0$ to $2\pi$
I'm defining branch cut functions, and I'm using $\arg(z)$ as a building block. So I just spent an hour at the whiteboard assuming that $\arg(z)$ goes from $0$ to $2\pi$, and then I implement the code,...