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Thread: group homomorphism

  1. November 21st 2009, 08:52 PM #1
    apple2009
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    group homomorphism

    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; November 21st 2009 at 09:04 PM. Reason: Changed post title
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  2. November 21st 2009, 09:13 PM #2
    Chris L T521
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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. November 22nd 2009, 01:18 AM #3
    tonio
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    Quote Originally Posted by apple2009 View Post
    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 |z_1z_2|=|z_1||z_2|\,\,\,\forall\,z_1\,,\,z_2\in\m athbb{C} ...piece of cake.

    Tonio
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