# 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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### ComplexExpand of Hypergeometric function

I would like to take the derivative of the absolute-squared value of a hypergeometric function and plot the result, for real arguments ...
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### Argument of a complex number with assumptions

I am trying to calculate the argument of a complex number: Arg[Cos[y]*Exp[I x]] where both x and y are real. The solution is clearly x, but I can't get it with ...
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### Possible bug in ResidueSum

Trying a new command of version 13.1 ResidueSum, I obtain FunctionMeromorphic[{(x^2 - x + 2)/x, Abs[x] > 5}, x] ...
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### Modulus square of an complex expression

I have an expression: E^(I*((-k)*x + \[Xi] - (t + 1/2)^y/(\[Beta]*Subscript[b, 2]*(Subscript[a, 2] + 2*k*Subscript[b, 2])))) I want to get modulus square of this ...
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### Simplification of complex number factors out an extra i

When I evaluate Simplify[ - a - I Sqrt[3] a - b - I Sqrt[3] b ] Mathematica returns -I (-I + Sqrt[3]) (a + b) Personally, I ...
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### ComplexExpand over various imaginary parts? [closed]

I have an equation a=(c+ I d); b=(e+ I f); I want to solve dd=(a C0 * b K C0)/(a C0 + b K C0); both e and f are imaginary ...
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### Solving a complex value coupled ODEs with NDSolve

I am a very beginner in Mathematica and I am trying to solve a complex value coupled ODEs with NDSolver. The equations would be like 1 where u refers to u(t) and a refers to a(t), other symbols such ...
49 views

### How do I get the complex conjugate of my interpolation?

I import an interpolation from C++ into mathematica which I then modify. Is there a way to obtain the conjugate of the interpolation? Or do I need to use $(f g)^* = f^* g^*$ and export the conjugated ...
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### ComplexExpand no longer assumes Derivative[__][__][__] as real

Bug introduced after 11.3, in or before 12.3, persisting through 13.0. Consider the following sample: {Re, Im}[u'[t]] // Through // ComplexExpand In v9.0.1 ...
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1 vote
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### Issue with using complexplot with Nearest

I have been trying to create a certain fractal with Mathematica but the main issue is that if I try and do something like ...
1 vote
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### Solve 2x2 complex unitary matrix with constains using Solve does not work

I have a 2x2 complex-valued matrix, $U=\pmatrix{U_{1,1}e^{i\theta_{1,1}}&U_{1,2}e^{i\theta_{1,2}}\\ U_{2,1}e^{i\theta_{2,1}}&U_{2,2}e^{i\theta_{2,2}}}$ which I must impose two ...
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1 vote
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### NDSolve for complex pde

My goal is to use NDSolve to solve the complex pde $F(z,t)$ with complex derivative $\partial_{z}=\frac{1}{2}(\partial_{x}-i \partial_{y}).$ The equation can be ...
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### Unable to simplify exponential expression to its simplest form of trigonometric expression by Euler's formula

Applying "FullSimplify" fails to simplify the following expressions: Input: ...
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### Plotting a long and complex airy function

I try to plot an Airy function ...
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### Roots of a transcendental equation with unknown a complex number

I am trying to solve a problem and I got stuck with a complicated transcendental equation. I intend to find these roots. Here, $\omega$ is a complex number, whose imaginary part can be positive or ...
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### WolframClient output convert to python complex array

I encountered the following issue with WolframClient. I have a my.function file which contains some function that takes some ...
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### Getting the "correct" branch of a complex function

This stuff always trips me up. I'm trying to plot a function and I think that the plot looks good in one region and isn't really what I'm expecting in another: The right side of the plot is what I am ...
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### Theory behind CountRoots

According to this page, one can compute the number of zeros of a meromorphic function over an interval in Mathematica. I am working with univariate functions of x, which are meromorphic elementary ...
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### Display Conjugate[x_] as a long overbar permanently

In TraditionalForm output, I would like to have Conjugate be always displayed as an overbar, not an asterisk superscript. In particular for complicated expressions like ...
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### Evaluation involving complex conjugates

I was trying to write an expression involving Conjugate. To create a minimal example, however, I have reduced it down to these expressions. ...
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### Plotting the image of $\Omega=\{z=x+iy \in \Bbb C \mid 1 \le x \le 2, 4\pi \le y \le 7\pi \}$ under $f(z)=e^z$

I'm trying to plot the image of the the set $\Omega=\{z=x+iy \in \Bbb C \mid 1 \le x \le 2, 4\pi \le y \le 7\pi \}$ under $f(z)=e^z$, but I cannot find right function to do this from the docs. Could ...
1 vote
81 views

### Divide by zero warning: Actual division by zero or spurious?

I have the following code that calculates the gain of an amplifier ...
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### Mathematica is messing around with absolute values and sqrts of complex numbers?

I know that $$\begin{pmatrix}0&Z\\Z^*&0\end{pmatrix} \quad\text{has eigenvalues}\quad \lambda_\pm=\pm|Z|$$ but Mathematica gives me ...
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### How to draw a tangent line for complex function?

I'm new with Mathematica and I have a problem with that, It would be great if you could help me with that. I try to draw a maximum slope of a plot in the same diagram using resource function tangent ...
59 views

### Simplifying a power of complex exponential quotient

I have an expression of the form $(\frac{-1+e^{i\,N\,\phi}}{-1+e^{i \phi}})^n$. I want to use mma to hopefully simplify it. I have tried ComplexExpand[], PowerExpand[] with simplifying assumption in ...
1 vote
60 views

### How do I plot different parts of a same function?

Let's say that I got a complex function $f$ of a real variable $x$, i.e. $f(x)$. Suppose that I want to plot the real part of $f$, i.e. $\Re(f(x))$. My question is: should I enclose ...
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### Solution this problem to illustrate the conformal mapping [duplicate]

Find the mapping of circle using confirmal mapping ( joukowski tansformation method) Assume w= z+1/z 〖z=re〗^iθ = 〖r(cosθ+isinθ)〗^1 ( a Circle with radius r and center (0,0))
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### Some help for rewriting this complex function [closed]

I have here a complex function in which z =x+ I y must be filled in f[z_] := E^(-z^2) By hand : ...
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### A famous Integral from Cauchy deriving, how? [closed]

A example of calculating line integrals in the complex plane Integrate[Cos[2*b*x]/E^x^2, {x, 0, Infinity}] = $\frac{1}{2} \sqrt{\pi } e^{-b^2}$ ( this is the famous ...
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### Mathematica not assuming real parameters

I have this expression: Eqn = (Cgd rg)/(Cgd+Cgs)+(Cgs rg)/(Cgd+Cgs)-I/(w (Cgd+Cgs)) When I try to evaluate it: ...
170 views

### Complex Map Using ComplexRegionPlot

I am self-studying complex analysis using Dennis Zill's, A First Course in Complex Analysis. I'm a bit stuck on one of the exercises in Chapter 2.4, which asks us to find the image of the region shown ...
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