# Doubt about rotation isometry on the complex plane

1. Nov 14, 2014

### PcumP_Ravenclaw

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...

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2. Nov 15, 2014

### HallsofIvy

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!

3. Nov 15, 2014

### PcumP_Ravenclaw

Oops sorry!!.

The missing scan is in this attachement.

danke.

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4. Nov 21, 2014

### Fredrik

Staff Emeritus
"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.