arguments and modulus

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Given: Let x = r(cos u + i sin u)

           Let y = t(cos v + i sin v)

Prove that xy = rt(cos(u+v) + i sin(u+v))

Provide a correct proof that includes written justification for each step showing the following:

1.  The angle (or argument) of the product xy is (u + v).

2.  The radius (or modulus) of the product xy is rt.

Note: Show the computation of their product and rewrite using algebraic properties. Make sure to justify each and every step of your work by citing the property or law you are following.

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