Let w=\frac{\sqrt{3}+i}{2} and z=\frac{-1+i \sqrt{3}}{2}, where i=\sqrt{-1}. Find the number of ordered pairs (r, s) of positive integers not exceeding 100 that satisfy the equation i \cdot w^{r}=z^{s}.
Let w=\frac{\sqrt{3}+i}{2} and z=\frac{-1+i \sqrt{3}}{2}, where i=\sqrt{-1}. Find the number of ordered pairs (r, s) of positive integers not exceeding 100 that satisfy the equation i \cdot w^{r}=z^{s}.