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Visualize the phase of complex square root with complicated cut

Update Here's a simplified numerical way, by integrating an ODE without branch points from the origin to $z$, determining the sign by whether the path crosses the branch cut (update 2: originally, I ...
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12 votes

Visualize the phase of complex square root with complicated cut

Edit3: Added a ComplexContourPlot of level curves over radial branch region. See below With these problems I find it helpful to draw the function in its entirety then decide how to cut out an ...
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9 votes

Visualize the phase of complex square root with complicated cut

Perhaps you can use ComplexPlot (since v12) ...
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1 vote

How can I reduce this complex exponent expression to real expression?

The last two terms can be simplified to real as follows FullSimplify[-(c - d I) E^((a + b I) t) - (c + d I) E^((a - b I) t)==-2 E^(a t) (c Cos[b t] + d Sin[b t])]/. ...
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2 votes

How can I visualize this complex geometry with mathematica?

I do not know if I understood you right. Can modify as needed. ...
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2 votes
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How can I visualize this complex geometry with mathematica?

What you are trying to achieve seems functionally equivalent to showing graphically that $\lim_{\theta\to 0}\frac{\sin \theta}{\theta}=1$. Here is an example to achieve that: ...
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1 vote

How can I reduce this complex exponent expression to real expression?

This is a problem created by using machine numbers. These are seldom 100% accurate, they are most of the time an approximation. And if you have an expression like: x - Conjugate[x] it is possible that ...
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3 votes
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How can I reduce this complex exponent expression to real expression?

Rationalize[expr, 0] // Im // ComplexExpand 0. It means that expr is real. ...
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2 votes

How to better display the data using ComplexListPlot?

Do you have any idea to display it better and easier to see the data One option is to use PlotStyle and change the point size? ...
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7 votes
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How to get the graph of this function?

Under the working assumption that $\phi$ is a real variable from 0 to 2 $\pi$, one way to go about it is the following: ...
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9 votes
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How to write an easy Conjugate Function that just replaces i -> -i

Replace acts on the full form of an expression, not the displayed form. The full form of your expression: expr = I (a + 0.5123 I b - 1.2332 I c); expr // FullForm Therefore a complex number is ...
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6 votes

Smallest positive real solution with InverseWeierstrassP

Instead of playing with numerical solvers, we can exploit a canonical exact approach. Since the Weierstrass elliptic function $\wp$ is doubly periodic, taking an inverse of it makes sense only locally ...
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1 vote

How to solve equations in Gaussian integers modulo p

Since $p$ is prime, this equation only needs to be solved within finite field. Depending on $p$, if $p \equiv 1 \space mod \space 4$, then $\sqrt{-1}$ has good reduction on $\mathbb{F_p}$, gaussian ...
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0 votes

How to solve PDEs for function $\Psi(z,\bar{z})$ dependent on independent variables $z,\bar{z}$? (Wirtinger derivatives)

I will only discuss the test case. An external reference is this PDF by Michael Stone. Some formulas for the Poincare disk model are on this Wikipedia page. Translation to $x,y$ coordinates. Here $z = ...
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2 votes

Square root of complex exponenial does not simplify

which should simplify to simple (1+2Nph) One way to simplify this is to to simplify with side relation ...
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0 votes

Plot image of complex function

This has been covered before, but one (of many) ways to do this is: ...
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  • 199
4 votes
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Interpreting DirectedInfinity

General discussion of DirectedInfinity In the complex plane, a ray can go off to infinity at any angle. DirectedInfinity[z] ...
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