# group homomorphism

• November 21st 2009, 09:52 PM
apple2009
group homomorphism
Show the function f: *→(positive) given by f(a+bi)=(a²+b²)^(1/2) is a group homomorphism.
• November 21st 2009, 10:13 PM
Chris L T521
Quote:

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 $\mathbb{R}$?
• November 22nd 2009, 02:18 AM
tonio
Quote:

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