Question

有一种新定律:i的平方为-1,i的三次方为-i,则i的2007次方为多少?i的2008次方为多少?

Answer 1

i^2 = -1

i^3 = -i

i^4 = (i^2)^2 = 1

所以i^2007 = (i^4)^501 * i^3 = -i

i^2008 = i^2007 * i = -i^2 = 1