I need to find an isomorphism between the group of orientation preserving rigid motions of the plane (translations, rotations) and complex valued matrices of the form(adsbygoogle = window.adsbygoogle || []).push({});

a b

0 1

where |a|=1.

I defined an isomorphism where the rotation part goes to e^it with angle t and the translation by l=ax+by to b=a+bi. But the multiplication doesn't work out.

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# Homework Help: Find an isomorphism between the group of orientation

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