simplify the following

Question

i³⁰

Answer 1

i = √-1

i² = -1

i³ = -i

i⁴ = 1

 

Now the values repeat

 

i⁵ = i⁴ · i = 1 · i = i

i⁶ = i⁴ · i² = 1 · -1 = -1

i⁷ = i⁴ · i³ = 1 · -i = -i

i⁸ = i⁴ · i⁴ = 1 · 1  = 1

 

i³⁰ = (i⁴)⁷ · i² = -1