How to verify if the groups $(RR,+)$ and $(CC$ * $,*)$ are isomorphic?

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Answer 1 · 2017-04-22T08:23:00

See explanation...

Note that $(CC^*, *)$ contains a non-identity element that is self inverse, namely:

$(-1)*(-1) = 1$

whereas all non-identity elements in $(RR, +)$ are not self inverse:

If $x != 0$ then $x+x != 0$

So the two groups cannot be isomorphic.

How to verify if the groups (RR,+)(RR,+) and (CC(CC*,*),*) are isomorphic?