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.
1,412 questions
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Visualizing Different Coordinate Representations of Complex Numbers
As a beginner with Mathematica, I apologize if this question is too basic. I would like to show introductory students that a complex number can be represented in several different coordinate systems ...
- 867
4
votes
1
answer
141
views
Visualizing multiple paths to infinity in the complex plane using Mathematica [closed]
Hello everyone — I’m reading about the extended complex plane and the “point at infinity,” and I find the geometric picture quite helpful. According to this text, in the complex plane $z \in \mathbb{C}...
- 867
2
votes
5
answers
213
views
How can I generate the $z^2$ grid-mapping diagram (rectangular grid → curved grid)?
I would like to generate a diagram in Mathematica showing how the mapping
\begin{equation}
w = z^2
\end{equation}
transforms a rectangular grid in the complex $z$-plane into a curved grid in the $w$-...
- 867
3
votes
3
answers
247
views
0
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0
answers
61
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ComplexExpand on BesselJ
I know ComplexExpand assumes its variables are real by default. However, when applied to BesselJ function, it is different. For ...
Qiang Lu
1
vote
0
answers
81
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Replacement of I to -I not working [duplicate]
Let
$f(x) = A \exp(i k x) + B \exp (-i k x)$.
If we replace every $i$ by $-i$, we are supposed to get
$g(x) = A \exp(-i k x) + B \exp (i k x)$.
However, the Mathematica code does not work as expected.
...
- 73
3
votes
2
answers
199
views
Simplifying fractions with complex numbers
How can I cajole Mathematica to transform
(a+b*I)/(c+d*I)
into
((a*c+b*d)+I*(b*c-a*d))/(c^2+d^2)
I tried the following, but it ...
- 231
1
vote
1
answer
182
views
Find real and imaginary parts of a complex series
I have the following complex series:
$$S=\sum _{n=0}^{\infty} \frac{3\,a^n }{(2n+1) (2n+3) \left(1+\dfrac{b}{x+iy }\right)^{2n+1}}\left(\frac{t}{x+i y}\right)^{2n}$$
where $a,b,t$ are real.
This ...
- 1,038
0
votes
1
answer
176
views
Plotting branch cut along `Im[z]=0` axis
I have expressions $\log\frac{z}{z-1}$ and $\frac{1}{z \left( 1 + W_0\left(-\frac{1}{e z}\right) \right)}
$ visualized below. There's a branch cut along the Im[z]=0 ...
- 7,681
1
vote
1
answer
305
views
How can I evaluate limit of ArcTanh with complex Tan as argument? [closed]
How can I evaluate this limit?
Limit[ArcTanh[((-5 + I Sqrt[23]) Tan[x/2])/Sqrt[58 - 2 I Sqrt[23]]],
x -> π]
Mathematica returns Indeterminate. The expected ...
- 1,758
1
vote
1
answer
172
views
Obtain the phase portrait of an array
I am trying to plot the phase portrait of a complex function of complex arguments on Mathematica. This is usually quite simple in the new version, through the use of ...
- 13
0
votes
1
answer
150
views
Complex equation ReImPlot
I have following equation $\frac{x^2}{\text{R}}+\frac{y \log \left(\frac{i x-i y+1}{-i x-i y+1}\right)}{2 x \left(1+\frac{i \log \left(\frac{i x-i y+1}{-i x-i
y+1}\right)}{2 x}\right)}+1 = 0$
...
- 1
0
votes
3
answers
317
views
Visualize the contour for $\oint_{|z|=2} \frac{1}{z^2+1}\,dz$ with two enclosed poles
I solved the following Integral
$$
\oint_{|z|=2} \frac{1}{z^2+1}\,dz
$$
and in my proof, I factor $z^2+1=(z-i)(z+i)$, so the function has simple poles at $z=i$ and $z=-i$, both inside the contour $ |z|...
2
votes
2
answers
165
views
Advice for solving a system of complex equations
I'm interested in investigating the following function f[w].
...
- 121
3
votes
3
answers
316
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Calculate the limit of a complex function [closed]
Let $f(z)=\frac{x}{x+y}+\frac{y^2+y}{x+y}i. $ Find $\displaystyle{\lim_{z \to 0}{f(z)}}.$
As $z\rightarrow 0$ along real axis: $z=x+0i$
$$\displaystyle{\lim_{x \to 0}{\frac{x}{x}}}=1$$
As $z\...