Loser66
  • Loser66
Show that \(\phi(t) = cis t\) is a group homomorphism of the additive group\(\mathbb R\) onto the multiplicative group T={z : |z|=1}\) Please help.
Mathematics
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SOLVED
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katieb
  • katieb
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Loser66
  • Loser66
Is it not that the function f maps the coordination of a point to itself in unit circle?
Zarkon
  • Zarkon
show \[\phi(a+b)=\phi(a)\phi(b)\]
Loser66
  • Loser66
I know how to show it is a homomorphism. I want to make sure about the map

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Zarkon
  • Zarkon
yes it maps to the unit circle in the complex plane
Loser66
  • Loser66
Define: S := additive group R T as it is f: S --> T \(z=cis t\mapsto |z|\) right?
Loser66
  • Loser66
If it is so, it turns to easy, right? hehehe.... since |cis t| = 1.
Loser66
  • Loser66
@Zarkon Thank you so much.
Zarkon
  • Zarkon
yes...very easy

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