Doubt about rotation isometry on the complex plane

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Discussion Overview

The discussion revolves around the concept of rotation isometry on the complex plane, specifically addressing questions about certain mathematical expressions and definitions related to the topic. Participants seek clarification on the implications of specific statements and the derivation of equations presented in an attachment.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests an explanation for the condition ## r(z) = z ## and its significance in the context of rotation isometry.
  • Another participant points out that the validity of statements hinges on the truth of an unspecified condition referred to as "(ii)," indicating a lack of clarity in the discussion.
  • A participant clarifies that "r is not the identity" means that there exists at least one complex number z for which the function r does not return z, implying that r is not the identity map.
  • There is a request for clarification on how the line ## L = 0.5*b + ρe^{θ/2} ## was derived, indicating a need for further explanation of this mathematical expression.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the unspecified condition "(ii)" and its implications, suggesting that the discussion remains unresolved on this point. There is also a lack of consensus on the derivation of the mathematical expression mentioned.

Contextual Notes

The discussion highlights missing assumptions related to the condition "(ii)" and the derivation of specific equations, which are not fully explained in the provided context.

PcumP_Ravenclaw
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Dear All,
In the 2nd paragraph of the attachment can you please explain to me why we are trying to make ## r(z) = z ##

and what does "As r is not the identity..." mean??

and how did the line ## L = 0.5*b + ρe^{θ/2} ## come about?

Danke...
 

Attachments

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The second sentence starts "If (ii) Is true" so everything said here depends upon "(ii)" being true but we don't know what "(ii)" is!
 
Oops sorry!.

The missing scan is in this attachement.

danke.
 

Attachments

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"r is not the identity" means "r is not the identity map", which means "r is not the unique function f such that f(z)=z for all z". So there's at least one complex number z such that r(z)≠z.
 

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