Annoying Imaginary Friends

Algebra Level 3

i0!+i1!+i2!++i100!=?\large { i }^{ 0! }+{ i }^{ 1! }+{ i }^{ 2! }+\cdots +{ i }^{ 100! }= \, ?

Clarifications:

  • i=1i = \sqrt{-1} .

  • !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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