$k$ in the expressions
                \[
                \arg\left(z_1z_2\right) = \left(\theta_1 + \theta_2\right)+ 2n\pi\quad (n\in \Z)
                \]
                and 
                \[
                \arg\left(z_1\right) =\theta_1 + 2k\pi\quad (k\in \Z)
                \]
                Now, since 
                \[
                \left(\theta_1 + \theta_2\right)+ 2n\pi = \theta_1 + 2k\pi + \left[\theta_2 + 2(n-k)\pi\right],
                \]
                equation (\ref{arg-product}) is