The 4n+ 1 power of I = the 4th power of I times I, the 4th power of I equals 1, the nth power of 1 equals 1, and 1 times I equals I, so the 4n+ 1 power of I equals I.

The 4n+2 power of I =- 1.

The 4n+2 power of I is equal to I times the 4n+ 1 power of I times I equals-1, so the 4n+2 power of I equals-1.

I =-I to the power of 4n+3.

The 4n+3 power of I is equal to the 4n+2 power of I multiplied by I, so it is equal to-i.