Hi I'm doing some exercises on homorphisms and the first question is:

Show

p:C^*--->R, p(z)=log|z| (z is in C)

is a homorphism.

I know the method p(ab)=p(a)p(b) but how can I tell from this question which binary operations the groups use to prove it? I get this problem in other areas aswell. I thought maybe the * meant multiplicative and no * meant addition but in my notes it says the * means C\0.

Thanks for any help.