An algebra problem by Alexander Koran

Algebra Level 3

\[\large \prod_{n=1}^{2017} i^{a_n}\]

Find the value of the product above, where \(a_n=n^n+n!\).

\(\)
Notations:

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