List questions from mobius-transformation

Published on 24 Oct 2020 - 9:53

52

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Is $\left\{z\in\Bbb C\;:\;\left|\frac{\epsilon}z-a\right|<r\right\}$ a circle?

Published on 29 Oct 2020 - 22:32

73

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General formula for center and radius of the circle $\left|\frac b{z-c}-a\right|=r$

Published on 03 Nov 2020 - 21:43

457

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Solve the equation $y=\frac{ax + b}{cx + d}$ for $x$, noting where the solution assumes $ad-bc\ne 0$

Published on 09 Nov 2020 - 23:56

135

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How to recognize if a Möbius transformation includes an 'inversion' operation?

Published on 10 Nov 2020 - 22:32

129

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Find a suitable Möbius transformation that maps $X=\{z|\ |z|<1, |z-q/2|<q/2\}$ onto the annulus $Y=\{z|\ p<|z|<1\}$ for some $p,q\in(0,1)$

Published on 13 Nov 2020 - 13:32

792

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biholomorphically mapping upper unit disk to unit disk

Published on 15 Nov 2020 - 9:33

188

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Inversion of conics

Published on 15 Nov 2020 - 9:48

107

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Is $GL_2(\mathbb{C})\cong \hat{\mathbb{C}}\times \mathbb{C}\times \mathbb{C}^\times \mathbb{C}^$?

Published on 17 Nov 2020 - 14:14

183

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$f$ meromorphic prove that $f$ is not constant

Published on 25 Mar 2026 - 21:47

79

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Kernel of Möbius transformation

Published on 26 Nov 2020 - 15:29

371

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Show that the Mobius transformations form a group.

Published on 03 Dec 2020 - 20:30

59

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Demonstrate the statement in section 3.I.3 on the decomposition of the Möbius transformations.

Published on 04 Dec 2020 - 0:34

2.1k

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Show that the Möbius transformations forms a group!

Published on 04 Dec 2020 - 22:14

241

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Particular holomorphic mappings of the Riemann sphere to itself

Published on 04 Dec 2020 - 23:48

List Question

Finding a specific disk automorphism.

Is $\left\{z\in\Bbb C\;:\;\left|\frac{\epsilon}z-a\right|<r\right\}$ a circle?

General formula for center and radius of the circle $\left|\frac b{z-c}-a\right|=r$

Solve the equation $y=\frac{ax + b}{cx + d}$ for $x$, noting where the solution assumes $ad-bc\ne 0$

How to recognize if a Möbius transformation includes an 'inversion' operation?

Find a suitable Möbius transformation that maps $X=\{z|\ |z|<1, |z-q/2|<q/2\}$ onto the annulus $Y=\{z|\ p<|z|<1\}$ for some $p,q\in(0,1)$

biholomorphically mapping upper unit disk to unit disk

Inversion of conics

Is $GL_2(\mathbb{C})\cong \hat{\mathbb{C}}\times \mathbb{C}\times \mathbb{C}^\times \mathbb{C}^$?

$f$ meromorphic prove that $f$ is not constant

Kernel of Möbius transformation

Show that the Mobius transformations form a group.

Demonstrate the statement in section 3.I.3 on the decomposition of the Möbius transformations.

Show that the Möbius transformations forms a group!

Particular holomorphic mappings of the Riemann sphere to itself

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