What is i^19?

i^{4n+ 1} = i

i^{4n + 2} = -1

i^{4n + 3} = -i

i^{4n + 4} = 1

Where i is an integer > 0

i¹⁹ can be written as i^{4(4) + 3}, so it equals  -i

Another way to figure this is to to divide the power on i by 4.

If the remainder = 1, then the answer is i

If the remainder = 2, then the answer is -1

If the remainder = 3, then the answer is -i

If the remainder = 0, then the answer is 1