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  1. #1
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    group homomorphism

    Show the function f: *→(positive) given by f(a+bi)=(aČ+bČ)^(1/2) is a group homomorphism.
    Last edited by mr fantastic; November 21st 2009 at 09:04 PM. Reason: Changed post title
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by apple2009 View Post
    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}?
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  3. #3
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    Quote Originally Posted by apple2009 View Post
    Show the function f: *→(positive) given by f(a+bi)=(aČ+bČ)^(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
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