power of i

Question

i⁸²⁰

 

i⁶⁰¹

 

i⁵¹⁰

 

i³²⁷

Answer 1

just divide the exponent by 4 and keep the REMAINDER (0, 1, 2 or 3) as the exponent of i; these powers are cyclical and equal 1, i, -1 and -i, respectively.