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 DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
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Plotting a dispersion curve with complex wavevectors [duplicate]

I want to reproduce a dispersion curve from P. Zou's thesis found here: http://www.ipd.anl.gov/anlpubs/2001/06/39620.pdf on Pg. 31, Eq. 2.13. The problem is, the code below only gives values for the ...
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Please explain this unexpected code snippet behavior [duplicate]

Consider a function that maps a complex function z->f(z) to it's multivariable counterpart (x,y)->f(x,y) ...
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78 views

Why is PolyLog[] giving weird answers for ordinary values? [duplicate]

Possibly related to this question, but it seems slightly different: Strange behaviour of PolyLog Function Wikipedia says that for real s, z<1 should be real. So I was confused when MMa returned: ...
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Why does this integral have a complex result

I wanted to find the normalization of distribution F2 . ...
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68 views

Coding contour integration [duplicate]

I am struggling to understand contour integration. How would it be applied in Mathematica? I am hoping that if I see it written in Mathematica code, it will help me understand it. eg how would $$\int_\...
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827 views

Complex integrals and residues

I have a question. I try to integrate this function: Integrate[Exp[I k z]*Exp[-Sqrt[k^2 - A^2]x]*Exp[-k^2*L^2/4]/Sqrt[k^2 - A^2], {k, -Infinity, -A}] But ...
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137 views

Trouble fitting an explicitly complex model with the TransformedFit package

This is follow up from a previous question in which @Oleksandr R. suggested the use of a package he developed for splitting a model and data into real and imaginary parts to avoid a problem with ...
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Always the same problem with Conjugate [duplicate]

I want to compute something like : ...
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46 views

Check if a (possibly nested) list is real [duplicate]

I have a very large matrix of numbers. I want to check if all its entries are real. At the moment I am using realQ = And @@ Thread[Flatten[Im @ #] == 0] & Is ...
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How to add something like a shadow to my resulting figure? [duplicate]

after plotting this function: ...
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126 views

Can I numerically solve these equation in Mathematica? [closed]

I have this couple of equations : $ \partial_\mu \partial^\mu z^i + G^{i\bar{p}} (\partial_j G_{k\bar{p}} ) \partial_\mu z^j \partial^\mu z^k + G^{i\bar{j}} (\partial_{\bar{j}} G_{k\bar{l}} ) \...
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Image of the unit circle under a complex rational function

Let $$f(z)=\dfrac{z(z-a)}{(z-b)(z-c)(z-d)}$$ be a complex rational function with distinct non zero complex numbers $a,b,c$ and $d.$ I need to plot the image of the unit circle $S=\{z\in\mathbb{C} : ...
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199 views

ComplexPlot3D and essential singularities [closed]

I am trying to understand the behavior of the functions $$ f(z) = e^\frac{1}{z} \qquad \text{and} \qquad \frac{1}{f(z)} = \frac{1}{e^\frac{1}{z}} $$ in the neighborhood of $z=0$. From the power ...
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Ticks command is not working for one axis

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1answer
46 views

Simplifying complex expresion (without ComplexExpand or User defined rules) [closed]

Many times, I've struggled with simplifying complex expressions, such as this extraordinarily simple expression, and Mathematica wont do it: ...
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2answers
152 views

Plot a complex function as a vector along a curve

I have y a function of x and a parameter k. I use but don't really understand Plot[Evaluate@Table[y[x,k],{k,{.01,.02,3,4,6}}],{x,.171,300},PlotRange etc. to ...
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1answer
332 views

Evaluate complex exponential expression [closed]

I am trying to evaluate the modulus of the following expression. The expected result is 1.3. However, I tried Abs, ComplexExpand but still couldn't get it. Can anyone help me out? Thanks. 1/(1+e^(...
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212 views

Integrate is giving imaginary solution

I read through some of the previous posts on imaginary answers popping up due to integrals, but I was unable to find a solution to my similar problem. I have the following integral (reduced to its ...
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1answer
732 views

Real and Imaginary matrix

I have a 2 by 2 matrix T: {{x, y}, {-y, x}} where x is the real part of some complex number and y is the imaginary part of something complex number. Let's say z1 = ...
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1answer
150 views

What does mean |sin(z)|<=1? [closed]

I already know that the magnitude of sin(z) its equal to sqrt(sin^2(x)+sinh^2(y))
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1answer
283 views

How to convert this complex number to exponential form? [closed]

I have $Z = {\frac{2+i}{2-i}}$. I need to write it in exponential form, i.e. $Z = r*e^{i{\phi}}$. I simplified the given example to ${\frac{3 + 4i}{5}}$, i.e. $a={\frac{3}{5}}, b={\frac{4}{5}}$. ...
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302 views

How to solve a non-linear equation?

I am trying to solve the following non-linear equation: $\frac{i e^{-x^2} \sqrt{\pi } x}{K^2}+\left(-0.131251-0.0379031 x^2-0.0151154 x^4-0.0100462 x^6+0.5 \left(0.00273859 +0.0400003 K^2\right) x^8+(...
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1answer
658 views

how draw root locus in mathematica 9 for a special case

my closed loop transfer function is: H(s)=2exp(-q)/(1+exp(-2q)) q=sqrt((a+k*sqrt(s)+s)*s) , s=sigma+jw how can i draw root locus of H(s) as 'a' changes for ...
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Gives me a complex solution [closed]

A := DSolve[{D[((It - Ir) * x / L + Ir) * w''[x], {x, 2}] - p/Y, w[x] == 0, w'[0] == 0, w''[L] == M0/(Y*Ir), w'''[L] == -P/(Y*Ir)}, w[x], x] I want a real ...
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Help plotting or evaluating confluent hypergeometric function and a Gamma function, both with imaginary values [closed]

I have this confluent hypergeometric function $ \begin{equation} _{1}F_{1}\left( \frac{i}{2}x,1,ix \right) \end{equation}$ and this gamma function $ \begin{equation} \Gamma\left(...
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211 views

Can one use the new random matrices features of Version 11 in addressing a certain octonionic-based question?

I have cross-posted the question https://math.stackexchange.com/questions/2012301/can-one-test-an-octonionic-interpretation-for-a-conjecture-apparently-valid-in and https://physics.stackexchange....

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