In mathematics, the circle group, denoted by T {\displaystyle \mathbb {T} } or S 1 {\displaystyle \mathbb {S} ^{1}}, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C × {\displaystyle \mathbb {C} ^{\times }}, the multiplicative group of all nonzero complex numbers. Wikipedia