Considering two complex numbers $z_1$ and $z_2$ in the form $z=r(\cos(\theta)+i\sin(\theta))$
There is this formula $z_1 z_2=r_1 r_2 (\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2))$
So this relation should hold : $\arg(z_1 z_2)=\arg(z_1)+\arg(z_2)$
But if I consider $z_1=-1=\cos(\pi)+i\sin(\pi)$ and $z_2=i=\cos(\frac{\pi}{2})+i\sin (\frac{\pi}{2})$
$z_1 z_2=-i=\cos(-\frac{\pi}{2})+i\sin(-\frac{\pi}{2})$
While $\arg(z_1)+\arg(z_2)= \pi+ \frac {\pi}{2}=\frac{3 \pi}{2}\neq \frac{-\pi}{2}$
The angle is actually the same but I get two different results. Is this normal or am I missing something?
Thanks for your help