I can calculate i to any power very easily without using the TI-84+. Simply divide the power by 4. If the remainder is 0, then the answer is 1. If the remainder is 1 then the answer is i. A remainder of 2 yields -1 and a remainder of 3 yields -i.
Using the TI-84+, and in a + bi mode, i^6 = -1.
i^7 = -3E-13-i and since -3E-13 is so close to zero, you just use -i
i^40 = 1
i^41 = -1E-13+i and since -3E-13 is so close to zero, you just use i.
Sometimes it;s a simple answer. Sometimes it;s in scientific notation. Just Curious. It seems unnessary to me to display it any way except 1, i, -1, or -i.