## Multiplicative Groups of Real Numbers and Complex Numbers are not Isomorphic

## Problem 130

Let $\R^{\times}=\R\setminus \{0\}$ be the multiplicative group of real numbers.

Let $\C^{\times}=\C\setminus \{0\}$ be the multiplicative group of complex numbers.

Then show that $\R^{\times}$ and $\C^{\times}$ are not isomorphic as groups.