Let G = {e^itheta);theta in R}(adsbygoogle = window.adsbygoogle || []).push({});

Show that G is isomorphic to the group of rotations in the plane given by 2x2 matrices.

Define phi:G->R(theta)

1-1: Consider e^ix, e^iy in G

Assume phi(expix)) = phi(expiy)) and we want to show exp(iy)=exp(iy)

Group ofrotations R(theta) is the matrix:

cosx -sinx = cosy -siny

sinx cosx siny cosy

But that implies cosx = cosy

which is not necessarily true.

What's wrong here?

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# Homework Help: Show something's a group

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