12 pointssimplify i38. i −1 −i 1

Are you sure you've copied down the original problem exactly as given?  i38 = 38i can't be simplified.  Perhaps you meant i^38, which is a different matter.

Note that i^38 = i^32 * I^4 * I^2.

Note that i^0, i^4, i^8, etc., all equal 1.  Therefore,

i^38 = (1)(1)i^2 = 1*(-1) = -1 (answer)