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

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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 \( \sum_{n=1}^{25} i^{n !}=a+i b \), where \( i=\sqrt{-1} \), then \( a-b \), is
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(a) prime number
(b) even number
(c) composite number
(d) perfect number
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