I'm doing an exercise from my textbook of abstract algebra class. And the book answer says that $(\Bbb R,\cdot)$ is not a subgroup of nonzero complex numbers under multiplication. But I thought:
- The set of $\Bbb R$ does have $1$, which is the identity of nonzero complex numbers under multiplication.
- $\Bbb R$ is closed under multiplication.
- $\Bbb R$ does have inverse for each of its member.
Any hints or pointing out my mistakes are very appreciated!