# Homomorphism and First Isomorphism Theorem

Let R>0 be the group of positive real numbers under multiplication. Let CX be the group of nonzero complex numbers under mu!tiplication. Let S1 = {a + bi such that a^2 + b^2 = 1) be the subgroup of C consisting of all complex numbers of absolute value 1. Note that is normal in Cx since Cx is abelian. Prove that CX/S1 is isomorphic to R>0. [Hint: Find a homomorphism from Cx to R>0 and use the First Isomorphism Theorem.]

© BrainMass Inc. brainmass.com April 3, 2020, 4:12 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/homomorphism-first-isomorphism-theorem-104664

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Proof:

We ...

#### Solution Summary

Homomorphism and First Isomorphism Theorem are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19