Understanding the change in $\arg(z-i)$ around a closed curve containing the point $i$.

Question

I understand why, for any complex number $z=re^{i\theta}$, as $z$ goes once around a closed curved $C$, counterclockwise, enclosing the point 0, the principal argument of $z$ increases by $2\pi$.

I need help in understanding why the argument of $z-i=Re^{i\phi}$ changes by $2\pi$ when $z$ goes once around a closed curved enclosing the point $i$.