Foundations, part 6

Algebra Level 4

(i+3i+3)2020+(i3i+3)2017+1=?\large \left(\dfrac{i + \sqrt 3}{- i + \sqrt 3}\right)^{2020} + \left(\dfrac{i - \sqrt 3}{i + \sqrt 3}\right)^{2017} + 1 = \, ?


Clarification: i=1i=\sqrt{-1} denotes the imaginary unit.

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