Complex multiplicative group
= Complex multiplicative group
{title2=$\mathbb C^*$}
= Multiplicative group of nonzero complex numbers
{synonym}
The nonzero <complex numbers> form an <abelian group> under multiplication, with identity one and inverse $z^{-1}$. As a <topological group> it is isomorphic to $\mathbb R\times S^1$ by logarithmic modulus and phase. It appears naturally as a <Möbius pointwise stabilizer of two points>.