Rationaler Einheitskreis/In Qi/Ist Gruppe/Aufgabe

Zeige, dass die Menge

{}S_{\mathbb {Q} }^{1}={\left\{z\in \mathbb {Q} [{\mathrm {i} }]\mid \vert {z}\vert =1\right\}}\,

mit der Multiplikation in ${}\mathbb {Q} [{\mathrm {i} }]$ eine kommutative Gruppe

ist.

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