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, $8! = 1\times2\times3\times\cdots\times8$ .