Simplify each of the following powers of i. i^22

-1

Step-by-step explanation:

i^0 =1

i ^1 = i

i^2 =-1

i^3 = -i

It cycles through  by 4

so i^4 is back to 1

Take the power , divide by 4  and look to the chart for the remainder

If the remainder  is 0  then  i to that power is 1

                                1                                          i

                                2                                         -1

                                 3                                         -i

i^22

Take 22/4 = 5 remainder 2

The remainder is 2   so i^22 = -1