# Tagged Questions

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### Intuition for the limit of complex functions

We have intuition and somehow geometrical point of view about the limit in the Real functions.I mean we can think of the limit on the graph of the Real function and imagine how close we can get on the ...
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### Cross product in complex vector spaces

When inner product is defined in complex vector space, conjugation is performed on one of the vectors. What about is the cross product of two complex 3D vectors? I suppose that one possible ...
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### A complex function

I just need some help with the penultimate question of my coursework: Let $w=f(z)=\coth(z/2)$. Show that $w=f(z)=h(C) = (C+1)/(C-1)$ where $C=g(z)=e^z$. Find the image of the given points, ...
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### Complex sets of the form $|f(z)| = c$

I'm looking for information on sets of the form $|f(z)| = c$, possibly with additional restrictions (e.g. $|z| < d$). I can probably also assume that $f$ is as nice as you'd like. I'm interested ...
### Equation of the complex locus: $|z-1|=2|z +1|$
This question requires finding the Cartesian equation for the locus: $|z-1| = 2|z+1|$ that is, where the modulus of $z -1$ is twice the modulus of $z+1$ I've solved this problem algebraically ...
### If $0$, $z_1$, $z_2$ and $z_3$ are concyclic, then $\frac{1}{z_1}$,$\frac{1}{z_2}$,$\frac{1}{z_3}$ are collinear
If the complex numbers $0$, $z_1$, $z_2$ and $z_3$ are concyclic, prove that $\frac{1}{z_1}$,$\frac{1}{z_2}$,$\frac{1}{z_3}$ are collinear. I really can't seem to get anywhere on this problem, ...