What does i to the 413 power equal?

Answer 1

Consider:

i¹ = i

i² = -1

i³ = -i

i⁴ = 1

i⁵ = i

...

The cycle of {i, -1, -i, 1} repeats with a period of 4

413 mod 4 = 1, so i⁴¹³ = i