Show the function f: ℂ*→ℝ(positive) given by f(a+bi)=(aČ+bČ)^(1/2) is a group homomorphism.
Last edited by mr fantastic; Nov 21st 2009 at 09:04 PM. Reason: Changed post title
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Originally Posted by apple2009 Show the function $\displaystyle f:\mathbb{C}^*\rightarrow\mathbb{R}^+$ given by $\displaystyle f\!\left(a+bi\right)=\sqrt{a^2+b^2}$ is a group homomorphism. What are the operations on $\displaystyle \mathbb{C}$ and $\displaystyle \mathbb{R}$?
Originally Posted by apple2009 Show the function f: ℂ*→ℝ(positive) given by f(a+bi)=(aČ+bČ)^(1/2) is a group homomorphism. This is the same as showing that $\displaystyle |z_1z_2|=|z_1||z_2|\,\,\,\forall\,z_1\,,\,z_2\in\m athbb{C}$ ...piece of cake. Tonio
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