Dear all, can you please verify if my derivation of the algebraic formula for the rotation isometry is correct. The handwritten file is attached.(adsbygoogle = window.adsbygoogle || []).push({});

The derivation from the book (Alan F beardon, Algebra and Geometry) which is succinct but rather unclear is given below.

Assume that f (z) = az + b. If a = 1 then f is a translation. If a = 1,

then f (w) = w, where w = b/(1 − a), and f (z) − w = a(z − w). It is now

clear that f is a rotation about w of angle θ, where a = ## e^{iθ} ## .

danke....

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# Derivation of rotation isometry on the complex plane

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