Hello,
I would like to know whether the only non trivial involutary group isomorphism $f:(\mathbb{C}^{*},\times)\to(\mathbb{C}^{*},\times)$ is the complex conjugation or not. Thank you in advance.
Hello, I would like to know whether the only non trivial involutary group isomorphism $f:(\mathbb{C}^{*},\times)\to(\mathbb{C}^{*},\times)$ is the complex conjugation or not. Thank you in advance. 

closed as too localized by Qiaochu Yuan, Martin Brandenburg, quid, André Henriques, Andreas Thom Jul 22 '11 at 14:32This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


$z\mapsto \frac{1}{z}$ 


How about $$ z\mapsto \frac{z}{z^2}?$$ 

