Sum of four consecutive powers of \( i \) (iota) is zero. i.e., \( ...

Sum of four consecutive powers of \( i \) (iota) is zero. i.e., \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3}=0, \forall n \in I \).
\( \mathrm{P} \)
If \( \sum_{r=4}^{100} i^{r !}+\prod_{r=1}^{101} i^{r}=a+i b \), where \( i=\sqrt{-1} \), then \( a+75 b \), is
W
(a) 11
(b) 22
(c) 33