Are these groups? If so show it, and if not provide a counterexample.
The set of all complex numbers $x$ that have absolute value $1$, with operation multiplication. Recall that the absolute value of a complex number $x$ written in the form $x = a +bi$, with $a$ and $b$ real, is given by $|x| = |a+bi| = (a^2 + b^2)^{1/2}$.
The set of all complex numbers $x$ that have absolute value $1$, with operation addition.