Annoying Imaginary Friends

Algebra Level 3

\[\large { i }^{ 0! }+{ i }^{ 1! }+{ i }^{ 2! }+\cdots +{ i }^{ 100! }= \, ? \]

Clarifications:

\(i = \sqrt{-1} \).
\(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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