Math Help - group homomorphism

1. group homomorphism

Show the function f: *→(positive) given by f(a+bi)=(a²+b²)^(1/2) is a group homomorphism.

2. Originally Posted by apple2009
Show the function $f:\mathbb{C}^*\rightarrow\mathbb{R}^+$ given by $f\!\left(a+bi\right)=\sqrt{a^2+b^2}$ is a group homomorphism.
What are the operations on $\mathbb{C}$ and $\mathbb{R}$?

3. Originally Posted by apple2009
Show the function f: *→(positive) given by f(a+bi)=(a²+b²)^(1/2) is a group homomorphism.

This is the same as showing that $|z_1z_2|=|z_1||z_2|\,\,\,\forall\,z_1\,,\,z_2\in\m athbb{C}$ ...piece of cake.

Tonio