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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