                We can easily prove (\ref{arg-product}) by letting $\theta_1$ and $\theta_2$ denote any
                values of $\arg\left(z_1\right)$ and $\arg\left(z_1\right),$ respectively. 
                Then expression (\ref{product}) tells us that $\theta_1+\theta_2$ is 
                a value of $\arg\left(z_1z_2\right).$ If the values of 
                $\arg\left(z_1z_2\right)$ and $\arg\left(z_1\right)$ are specified, those values 
                correspond to particular choices of $n$ and 